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Comprehensive Review of Metaheuristic Algorithms (MAs) for Optimal Control (OCl) Improvement

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Abstract

Optimal control (OCl) can be traced back to the 1960s when it was utilised for solving an optimisation problem (OP). In the OCl technique, a stable controller can be obtained by optimising a cost function (CF). This means that the performance provided by an OCl technique is the best in any instance. Nevertheless, this performance is not unique. Additionally, the parameters are not optimal. As such, there is a need to improve the technique so that the performance and the parameters are optimal. It has many applications in different fields of study such as engineering. There exist different OCl techniques such as Linear Quadratic Gaussian (LQG), Model Predictive Control (MPCl), Kalman Filter (KF), Linear Quadratic Regulator (LQR), etc. LQR and LQG are among the OCl techniques that are becoming popular in the industry and the research community. These controllers can provide robust stability because of their outstanding properties. Robustness to modelling uncertainty and noise (particular to LQG), closed-loop stability, direct input control, optimal input control, etc., are some of the properties that lead to this robust stability provided by these controllers. Nevertheless, one of their major problems is the tuning method. Conventionally, these controllers are tuned using classical methods such as Bryson’s, analytical, trial-and-error, etc., methods. But these methods are associated with a lot of issues, such as time consumption, requiring experience and understanding of the problem at hand, lack of guaranteeing optimal values, etc., which lead to performance, stability, robustness, etc., problems. To solve these issues, researchers tend to use computational (optimisation) methods which proved to be more efficient. Consequently, a comprehensive state-of-the-art review of the recent studies that used computational methods for the improvement of OCl is presented in this paper. Different MAs that have been used to implement optimised LQR and LQG controls have been presented where the most used MAs are discussed in detail. The extent to which these MAs improved the control techniques is critically analysed. Additionally, optimised hybrids of these control techniques have been considered. Furthermore, the most controlled systems are discussed in detail including system modelling and state space representation derivation. The implementation modes of the techniques have been analysed. Some future research directions are also outlined. In essence, the work’s major goal is to provide a comprehensive guide for researchers on computational methods usage for OCl improvement using LQR and LQG as case studies.

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References

  1. Mohammed U, Karataev T, Oshiga O, Hussein S (2021) Optimal controller design for the system of ball-on-sphere: the linear quadratic Gaussian (LQG) case. IJEM 11:14–30. https://doi.org/10.5815/ijem.2021.02.02

    Article  Google Scholar 

  2. Siebenthal CD, Aris R (1964) Studies in optimization—VI the application of Pontryagin’s methods to the control of a stirred reactor. Chem Eng Sci 19:729–746. https://doi.org/10.1016/0009-2509(64)85085-5

    Article  Google Scholar 

  3. Sun H, Luo S, Sun Q et al (2020) Trajectory optimization for parafoil delivery system considering complicated dynamic constraints in high-order model. Aerosp Sci Technol 98:105631. https://doi.org/10.1016/j.ast.2019.105631

    Article  Google Scholar 

  4. Liu P, Liu X, Wang P et al (2019) Control variable parameterisation with penalty approach for hypersonic vehicle reentry optimisation. Int J Control 92:2015–2024. https://doi.org/10.1080/00207179.2018.1426882

    Article  MathSciNet  Google Scholar 

  5. Chen N, Luo S, Dai J et al (2020) Optimal control of iron-removal systems based on off-policy reinforcement learning. IEEE Access 8:149730–149740. https://doi.org/10.1109/ACCESS.2020.3015801

    Article  Google Scholar 

  6. Chen T, Lou J, Yang Y et al (2020) Vibration suppression of a high-speed macro-micro integrated system using computational optimal control. IEEE Trans Industr Electron 67:7841–7850. https://doi.org/10.1109/TIE.2019.2941136

    Article  Google Scholar 

  7. Li X, Dong L, Sun C (2021) Data-based optimal tracking of autonomous nonlinear switching systems. IEEE/CAA J Autom Sinica 8:227–238. https://doi.org/10.1109/JAS.2020.1003486

    Article  MathSciNet  Google Scholar 

  8. Liu J, Dong S, Hong J et al (2020) A fast iterative approach for optimal control of nonlinear systems. IFAC-PapersOnLine 53:7049–7054. https://doi.org/10.1016/j.ifacol.2020.12.451

    Article  Google Scholar 

  9. Naidu DS (2003) Optimal control systems. CRC Press, Boca Raton

    Google Scholar 

  10. Adelberger D, Giarré L, Ohtsuka T, Del Re L (2022) Optimal plug-and-control of unknown nonlinear systems. Eur J Control 64:100606. https://doi.org/10.1016/j.ejcon.2021.12.001

    Article  MathSciNet  Google Scholar 

  11. Kim J-H, Kim Y-H (2011) Motion control of a cruise ship by using active stabilizing fins. Proc Inst Mech Eng Part M 225:311–324. https://doi.org/10.1177/1475090211421268

    Article  Google Scholar 

  12. Nascimento LBP, Pinto VP, Amora MAB (2018) Harmony search algorithm with adaptive parameters to optimize the linear quadratic regulator design. IEEE Latin Am Trans 16:1862–1869. https://doi.org/10.1109/TLA.2018.8447350

    Article  Google Scholar 

  13. Ahmed M, Alsokhiry F, Abdel-Khalik AS et al (2021) Improved damping control method for grid-forming converters using LQR and optimally weighted feedback control loops. IEEE Access 9:87484–87500. https://doi.org/10.1109/ACCESS.2021.3089197

    Article  Google Scholar 

  14. Garone E, Sinopoli B, Goldsmith A, Casavola A (2012) LQG control for MIMO systems over multiple erasure channels with perfect acknowledgment. IEEE Trans Automat Contr 57:450–456. https://doi.org/10.1109/TAC.2011.2167789

    Article  MathSciNet  Google Scholar 

  15. Jung H, Jung D, Choi SB (2022) LQR control of an all-wheel drive vehicle considering variable input constraint. IEEE Trans Contr Syst Technol 30:85–96. https://doi.org/10.1109/TCST.2021.3051233

    Article  Google Scholar 

  16. Maity D, Mamduhi MH, Hirche S et al (2019) Optimal LQG control under delay-dependent costly information. IEEE Control Syst Lett 3:102–107. https://doi.org/10.1109/LCSYS.2018.2853648

    Article  MathSciNet  Google Scholar 

  17. Wu Y, Hamroun B, Le Gorrec Y, Maschke B (2021) Reduced order LQG control design for infinite dimensional port hamiltonian systems. IEEE Trans Autom Cont 66:865–871. https://doi.org/10.1109/TAC.2020.2997373

    Article  MathSciNet  Google Scholar 

  18. Xin G, Xin S, Cebe O et al (2021) Robust footstep planning and LQR control for dynamic quadrupedal locomotion. IEEE Robot Autom Lett 6:4488–4495. https://doi.org/10.1109/LRA.2021.3068695

    Article  Google Scholar 

  19. Kumare V, Jerome J (2016) Algebraic riccati equation based Q and R matrices selection algorithm for optimal LQR applied to tracking control of 3rd order magnetic levitation system. Arch Electr Eng 65:151–169. https://doi.org/10.1515/aee-2016-0012

    Article  Google Scholar 

  20. Bużantowicz W (2021) Tuning of a linear-quadratic stabilization system for an anti-aircraft missile. Aerospace 8:48. https://doi.org/10.3390/aerospace8020048

    Article  Google Scholar 

  21. Nocoń Ł, Grzyb M, Szmidt P et al (2022) Control analysis with modified LQR method of anti-tank missile with vectorization of the rocket engine thrust. Energies 15:356. https://doi.org/10.3390/en15010356

    Article  Google Scholar 

  22. Conte GYC, Marques FG, Garcia C (2021) LQR and PID control design for a pneumatic diaphragm valve. In: 2021 IEEE international conference on automation/XXIV congress of the Chilean association of automatic control (ICA-ACCA). IEEE, Valparaíso, pp 1–7

  23. Pourshaghaghi HR, Jaheh-Motlagh MR, Jalali A-A (2007) Optimal feedback control design using genetic algorithm applied to inverted pendulum. In: 2007 IEEE international symposium on industrial electronics. IEEE, Vigo, pp 263–268

  24. Mohammed U, Hussein SU, Usman M, Thomas S (2020) Design of an optimal linear quadratic regulator (LQR) controller for the ball-on-sphere system. IJEM 10:56–70. https://doi.org/10.5815/ijem.2020.03.05

    Article  Google Scholar 

  25. Mohammed U, Karataev T, Oshiga O et al (2021) Comparison of linear quadratic—regulator and Gaussian—controllers’ performance, LQR and LQG: ball-on-sphere system as a case study. IJEM 11:45–67. https://doi.org/10.5815/ijem.2021.03.05

    Article  Google Scholar 

  26. Trimpe S, Millane A, Doessegger S, D’Andrea R (2014) A self-tuning LQR approach demonstrated on an inverted pendulum. IFAC Proc Vol 47:11281–11287. https://doi.org/10.3182/20140824-6-ZA-1003.01455

    Article  Google Scholar 

  27. Huang X, Li P (2020) An Auto-tuning LQR based on correlation analysis. IFAC-PapersOnLine 53:7148–7153. https://doi.org/10.1016/j.ifacol.2020.12.525

    Article  Google Scholar 

  28. Saleem O (2023) An enhanced adaptive-LQR procedure for under-actuated systems using relative-rate feedback to dynamically reconfigure the state-weighting-factors. J Vib Control 29:2316–2331. https://doi.org/10.1177/10775463221078654

    Article  Google Scholar 

  29. Sir Elkhatem A, Naci Engin S (2022) Robust LQR and LQR-PI control strategies based on adaptive weighting matrix selection for a UAV position and attitude tracking control. Alex Eng J 61:6275–6292. https://doi.org/10.1016/j.aej.2021.11.057

    Article  Google Scholar 

  30. Katebi J, Shoaei-parchin M, Shariati M et al (2020) Developed comparative analysis of metaheuristic optimization algorithms for optimal active control of structures. Eng Comput 36:1539–1558. https://doi.org/10.1007/s00366-019-00780-7

    Article  Google Scholar 

  31. Burns RS (2001) Advanced control engineering. Butterworth-Heinemann, Oxford

    Google Scholar 

  32. Goel G, Hassibi B (2022) The power of linear controllers in LQR control. In: 2022 IEEE 61st conference on decision and control (CDC). IEEE, Cancun, pp 6652–6657

  33. Okyere E, Bousbaine A, Poyi GT et al (2019) LQR controller design for quad-rotor helicopters. J Eng 2019:4003–4007. https://doi.org/10.1049/joe.2018.8126

    Article  Google Scholar 

  34. Deng X, Sun X, Liu R, Wei W (2017) Optimal analysis of the weighted matrices in LQR based on the differential evolution algorithm. In: 2017 29th Chinese control and decision conference (CCDC). IEEE, Chongqing, pp 832–836

  35. Kumar EV, Jerome J, Srikanth K (2014) Algebraic approach for selecting the weighting matrices of linear quadratic regulator. In: 2014 international conference on green computing communication and electrical engineering (ICGCCEE). IEEE, Coimbatore, pp 1–6

  36. Elahi A, Gholizadeh A, Aghae A, Ghazinia M (2014) Linear quadratic gaussian control for upfc auxiliary stabilizer. SciInt(Lahore) 26:1535–1538

    Google Scholar 

  37. Skiena SS (2020) The algorithm design manual, 3rd edn. Springer, New York

    Book  Google Scholar 

  38. Harvey D, Hittmeir M (2022) A deterministic algorithm for finding r-power divisors. Res Number Theory 8:94. https://doi.org/10.1007/s40993-022-00387-w

    Article  MathSciNet  Google Scholar 

  39. Sabir Z, Baleanu D, Ali MR, Sadat R (2022) A novel computing stochastic algorithm to solve the nonlinear singular periodic boundary value problems. Int J Comput Math 99:2091–2104. https://doi.org/10.1080/00207160.2022.2037132

    Article  MathSciNet  Google Scholar 

  40. Sarmah DK, Kulkarni AJ, Abraham A (2020) Heuristics and metaheuristic optimization algorithms. In: Sarmah DK, Kulkarni AJ, Abraham A (eds) Optimization models in steganography using metaheuristics. Springer, Cham, pp 49–61

    Chapter  Google Scholar 

  41. Almubaidin MAA, Ahmed AN, Sidek LBM, Elshafie A (2022) Using metaheuristics algorithms (MHAs) to optimize water supply operation in reservoirs: a review. Arch Comput Methods Eng 29:3677–3711. https://doi.org/10.1007/s11831-022-09716-9

    Article  MathSciNet  Google Scholar 

  42. Negi G, Kumar A, Pant S, Ram M (2021) GWO: a review and applications. Int J System Assur Eng Manag 12:1–8. https://doi.org/10.1007/s13198-020-00995-8

    Article  Google Scholar 

  43. Tsai C-W, Chiang M-C (2023) Handbook of metaheuristic algorithms: from fundamental theories to advanced applications, 1st edn. Academic Press, New York

    Google Scholar 

  44. Samareh Moosavi SH, Bardsiri VK (2019) Poor and rich optimization algorithm: a new human-based and multi populations algorithm. Eng Appl Artif Intell 86:165–181. https://doi.org/10.1016/j.engappai.2019.08.025

    Article  Google Scholar 

  45. Singh MK (2012) A new optimization method based on adaptive social behavior: ASBO. In: Kumar MA, Kumar TVS (eds) Proceedings of international conference on advances in computing. Springer, New Delhi, pp 823–831

  46. Fadakar E, Ebrahimi M (2016) A new metaheuristic football game inspired algorithm. In: 2016 1st conference on swarm intelligence and evolutionary computation (CSIEC). IEEE, Bam, pp 6–11

  47. Razmjooy N, Khalilpour M, Ramezani M (2016) A new meta-heuristic optimization algorithm inspired by FIFA world cup competitions: theory and its application in PID designing for AVR system. J Control Autom Electr Syst 27:419–440. https://doi.org/10.1007/s40313-016-0242-6

    Article  Google Scholar 

  48. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. SIMULATION 76:60–68. https://doi.org/10.1177/003754970107600201

    Article  Google Scholar 

  49. Hatamlou A (2014) Heart: a novel optimization algorithm for cluster analysis. Prog Artif Intell 2:167–173. https://doi.org/10.1007/s13748-014-0046-5

    Article  Google Scholar 

  50. Moazzeni AR, Khamehchi E (2020) Rain optimization algorithm (ROA): a new metaheuristic method for drilling optimization solutions. J Petrol Sci Eng 195:107512. https://doi.org/10.1016/j.petrol.2020.107512

    Article  Google Scholar 

  51. Kaboli A, SHr, Selvaraj J, Rahim NA (2017) Rain-fall optimization algorithm: a population based algorithm for solving constrained optimization problems. J Comput Sci 19:31–42. https://doi.org/10.1016/j.jocs.2016.12.010

    Article  Google Scholar 

  52. TummalaSLV A, Ramakrishna NSS, Elavarasan RM et al (2022) War strategy optimization algorithm: a new effective metaheuristic algorithm for global optimization. IEEE Access 10:25073–25105. https://doi.org/10.1109/ACCESS.2022.3153493

    Article  Google Scholar 

  53. Zhang Y, Jin Z (2020) Group teaching optimization algorithm: a novel metaheuristic method for solving global optimization problems. Expert Syst Appl 148:113246. https://doi.org/10.1016/j.eswa.2020.113246

    Article  Google Scholar 

  54. Ghasemi M, Zare M, Zahedi A et al (2023) Geyser inspired algorithm: a new geological-inspired meta-heuristic for real-parameter and constrained engineering optimization. J Bionic Eng. https://doi.org/10.1007/s42235-023-00437-8

    Article  Google Scholar 

  55. Mirjalili S (2016) SCA: a sine cosine algorithm for solving optimization problems. Knowl-Based Syst 96:120–133. https://doi.org/10.1016/j.knosys.2015.12.022

    Article  Google Scholar 

  56. Sadollah A, Bahreininejad A, Eskandar H, Hamdi M (2013) Mine blast algorithm: a new population based algorithm for solving constrained engineering optimization problems. Appl Soft Comput 13:2592–2612. https://doi.org/10.1016/j.asoc.2012.11.026

    Article  Google Scholar 

  57. Anita YA (2019) AEFA: artificial electric field algorithm for global optimization. Swarm Evol Comput 48:93–108. https://doi.org/10.1016/j.swevo.2019.03.013

    Article  Google Scholar 

  58. Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179:2232–2248. https://doi.org/10.1016/j.ins.2009.03.004

    Article  Google Scholar 

  59. Abedinpourshotorban H, Mariyam Shamsuddin S, Beheshti Z, Jawawi DNA (2016) Electromagnetic field optimization: a physics-inspired metaheuristic optimization algorithm. Swarm Evol Comput 26:8–22. https://doi.org/10.1016/j.swevo.2015.07.002

    Article  Google Scholar 

  60. Su H, Zhao D, Heidari AA et al (2023) RIME: a physics-based optimization. Neurocomputing 532:183–214. https://doi.org/10.1016/j.neucom.2023.02.010

    Article  Google Scholar 

  61. Formato RA (2008) Central force optimization: a new nature inspired computational framework for multidimensional search and optimization. In: Krasnogor N, Nicosia G, Pavone M, Pelta D (eds) Nature inspired cooperative strategies for optimization (NICSO 2007). Springer, Berlin, pp 221–238

    Chapter  Google Scholar 

  62. Birbil Şİ, Fang S-C (2003) An electromagnetism-like mechanism for global optimization. J Global Optim 25:263–282. https://doi.org/10.1023/A:1022452626305

    Article  MathSciNet  Google Scholar 

  63. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680. https://doi.org/10.1126/science.220.4598.671

    Article  MathSciNet  Google Scholar 

  64. Černý V (1985) Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45:41–51. https://doi.org/10.1007/BF00940812

    Article  MathSciNet  Google Scholar 

  65. Kaveh A, Dadras A (2017) A novel meta-heuristic optimization algorithm: thermal exchange optimization. Adv Eng Softw 110:69–84. https://doi.org/10.1016/j.advengsoft.2017.03.014

    Article  Google Scholar 

  66. Mirjalili S, Gandomi AH, Mirjalili SZ et al (2017) Salp swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw 114:163–191. https://doi.org/10.1016/j.advengsoft.2017.07.002

    Article  Google Scholar 

  67. Saremi S, Mirjalili S, Lewis A (2017) Grasshopper optimisation algorithm: theory and application. Adv Eng Softw 105:30–47. https://doi.org/10.1016/j.advengsoft.2017.01.004

    Article  Google Scholar 

  68. Mirjalili S, Lewis A (2016) The whale optimization algorithm. Adv Eng Softw 95:51–67. https://doi.org/10.1016/j.advengsoft.2016.01.008

    Article  Google Scholar 

  69. Mirjalili S (2016) Dragonfly algorithm: a new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Comput Appl 27:1053–1073. https://doi.org/10.1007/s00521-015-1920-1

    Article  Google Scholar 

  70. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61. https://doi.org/10.1016/j.advengsoft.2013.12.007

    Article  Google Scholar 

  71. Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: González JR, Pelta DA, Cruz C et al (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74

    Chapter  Google Scholar 

  72. Oftadeh R, Mahjoob MJ, Shariatpanahi M (2010) A novel meta-heuristic optimization algorithm inspired by group hunting of animals: hunting search. Comput Math Appl 60:2087–2098. https://doi.org/10.1016/j.camwa.2010.07.049

    Article  Google Scholar 

  73. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Erciyes University, Kayseri

    Google Scholar 

  74. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern B 26:29–41. https://doi.org/10.1109/3477.484436

    Article  Google Scholar 

  75. Kennedy J, Eberhart R (1995) Particle swarm optimization. In: Proceedings of ICNN’95—international conference on neural networks. IEEE, Perth, pp 1942–1948

  76. Agushaka JO, Ezugwu AE, Abualigah L (2022) Dwarf mongoose optimization algorithm. Comput Methods Appl Mech Eng 391:114570. https://doi.org/10.1016/j.cma.2022.114570

    Article  MathSciNet  Google Scholar 

  77. Golalipour K, Faraji Davoudkhani I, Nasri S et al (2023) The corona virus search optimizer for solving global and engineering optimization problems. Alex Eng J 78:614–642. https://doi.org/10.1016/j.aej.2023.07.066

    Article  Google Scholar 

  78. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11:341–359. https://doi.org/10.1023/A:1008202821328

    Article  MathSciNet  Google Scholar 

  79. Ferreira C (2001) Gene expression programming: a new adaptive algorithm for solving problems. Complex Syst 13:87–129

    MathSciNet  Google Scholar 

  80. Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection, 1st edn. The MIT Press, Cambridge

    Google Scholar 

  81. Beyer H-G, Schwefel H-P (2002) Evolution strategies—a comprehensive introduction. Nat Comput 1:3–52. https://doi.org/10.1023/A:1015059928466

    Article  MathSciNet  Google Scholar 

  82. Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, 1st edn. MIT Press, Cambridge

    Google Scholar 

  83. Farasat A, Menhaj MB, Mansouri T, Moghadam MRS (2010) ARO: a new model-free optimization algorithm inspired from asexual reproduction. Appl Soft Comput 10:1284–1292. https://doi.org/10.1016/j.asoc.2010.05.011

    Article  Google Scholar 

  84. Askarzadeh A (2014) Bird mating optimizer: an optimization algorithm inspired by bird mating strategies. Commun Nonlinear Sci Numer Simul 19:1213–1228. https://doi.org/10.1016/j.cnsns.2013.08.027

    Article  MathSciNet  Google Scholar 

  85. Salcedo-Sanz S, Del Ser J, Landa-Torres I et al (2014) The coral reefs optimization algorithm: a novel metaheuristic for efficiently solving optimization problems. Sci World J 2014:1–15. https://doi.org/10.1155/2014/739768

    Article  Google Scholar 

  86. Fogel DB (1998) Artificial Intelligence through simulated evolution. In: Evolutionary computation: the fossil record. IEEE, pp 227–296

  87. Lourenço HR, Martin OC, Stützle T (2003) Iterated local search. In: Glover F, Kochenberger GA (eds) Handbook of metaheuristics. Springer, Boston, pp 320–353

    Chapter  Google Scholar 

  88. Mladenović N, Hansen P (1997) Variable neighborhood search. Comput Oper Res 24:1097–1100. https://doi.org/10.1016/S0305-0548(97)00031-2

    Article  MathSciNet  Google Scholar 

  89. Feo TA, Resende MGC (1989) A probabilistic heuristic for a computationally difficult set covering problem. Oper Res Lett 8:67–71. https://doi.org/10.1016/0167-6377(89)90002-3

    Article  MathSciNet  Google Scholar 

  90. Feo TA, Resende MGC (1995) Greedy randomized adaptive search procedures. J Global Optim 6:109–133. https://doi.org/10.1007/BF01096763

    Article  MathSciNet  Google Scholar 

  91. Glover F (1996) Ejection chains, reference structures and alternating path methods for traveling salesman problems. Discret Appl Math 65:223–253. https://doi.org/10.1016/0166-218X(94)00037-E

    Article  MathSciNet  Google Scholar 

  92. Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13:533–549. https://doi.org/10.1016/0305-0548(86)90048-1

    Article  MathSciNet  Google Scholar 

  93. Hu G, Guo Y, Wei G, Abualigah L (2023) Genghis Khan shark optimizer: a novel nature-inspired algorithm for engineering optimization. Adv Eng Inform 58:102210. https://doi.org/10.1016/j.aei.2023.102210

    Article  Google Scholar 

  94. Ezugwu AE, Agushaka JO, Abualigah L et al (2022) Prairie dog optimization algorithm. Neural Comput Appl 34:20017–20065. https://doi.org/10.1007/s00521-022-07530-9

    Article  Google Scholar 

  95. Agushaka JO, Ezugwu AE, Abualigah L (2023) Gazelle optimization algorithm: a novel nature-inspired metaheuristic optimizer. Neural Comput Appl 35:4099–4131. https://doi.org/10.1007/s00521-022-07854-6

    Article  Google Scholar 

  96. Hu G, Zheng Y, Abualigah L, Hussien AG (2023) DETDO: an adaptive hybrid dandelion optimizer for engineering optimization. Adv Eng Inform 57:102004. https://doi.org/10.1016/j.aei.2023.102004

    Article  Google Scholar 

  97. Zare M, Ghasemi M, Zahedi A et al (2023) A global best-guided firefly algorithm for engineering problems. J Bionic Eng 20:2359–2388. https://doi.org/10.1007/s42235-023-00386-2

    Article  Google Scholar 

  98. Abualigah L, Ekinci S, Izci D, Zitar RA (2023) Modified elite opposition-based artificial hummingbird algorithm for designing FOPID controlled cruise control system. IASC. https://doi.org/10.32604/iasc.2023.040291

  99. Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning, 1st edn. Addison-Wesley Longman Publishing Co. Inc, Boston

    Google Scholar 

  100. Jafari A, Khalili T, Babaei E, Bidram A (2020) A hybrid optimization technique using exchange market and genetic algorithms. IEEE Access 8:2417–2427. https://doi.org/10.1109/ACCESS.2019.2962153

    Article  Google Scholar 

  101. Kaleybar HJ, Davoodi M, Brenna M, Zaninelli D (2023) Applications of genetic algorithm and its variants in rail vehicle systems: a bibliometric analysis and comprehensive review. IEEE Access 11:68972–68993. https://doi.org/10.1109/ACCESS.2023.3292790

    Article  Google Scholar 

  102. El-Shorbagy MA, El-Refaey AM (2020) Hybridization of grasshopper optimization algorithm with genetic algorithm for solving system of non-linear equations. IEEE Access 8:220944–220961. https://doi.org/10.1109/ACCESS.2020.3043029

    Article  Google Scholar 

  103. Khafaji MJ, Krasicki M (2021) Uni-cycle genetic algorithm to improve the adaptive equalizer performance. IEEE Commun Lett 25:3609–3613. https://doi.org/10.1109/LCOMM.2021.3105640

    Article  Google Scholar 

  104. Chen P-Y, Chen R-D, Chang Y-P et al (2008) Hardware implementation for a genetic algorithm. IEEE Trans Instrum Meas 57:699–705. https://doi.org/10.1109/TIM.2007.913807

    Article  Google Scholar 

  105. Oh S, Yoon J, Choi Y et al (2022) Genetic algorithm for the optimization of a building power consumption prediction model. Electronics 11:3591. https://doi.org/10.3390/electronics11213591

    Article  Google Scholar 

  106. Drachal K, Pawłowski M (2021) A review of the applications of genetic algorithms to forecasting prices of commodities. Economies 9:6. https://doi.org/10.3390/economies9010006

    Article  Google Scholar 

  107. Lee S, Kim J, Kang H et al (2021) Genetic algorithm based deep learning neural network structure and hyperparameter optimization. Appl Sci 11:744. https://doi.org/10.3390/app11020744

    Article  Google Scholar 

  108. Abbasi M, Rafiee M, Khosravi MR et al (2020) An efficient parallel genetic algorithm solution for vehicle routing problem in cloud implementation of the intelligent transportation systems. J Cloud Comp 9:6. https://doi.org/10.1186/s13677-020-0157-4

    Article  Google Scholar 

  109. Skorpil V, Oujezsky V (2022) Parallel genetic algorithms’ implementation using a scalable concurrent operation in python. Sensors 22:2389. https://doi.org/10.3390/s22062389

    Article  Google Scholar 

  110. Ali Shah Tirmzi SA, Umar AI, Shirazi SH et al (2022) Modified genetic algorithm for optimal classification of abnormal MRI tissues using hybrid model with discriminative learning approach. Comput Methods Biomech Biomed Eng 10:14–21. https://doi.org/10.1080/21681163.2021.1956371

    Article  Google Scholar 

  111. Peng Z, Wang L, Tong L et al (2023) Multi-threshold image segmentation of 2D OTSU inland ships based on improved genetic algorithm. PLoS ONE 18:e0290750. https://doi.org/10.1371/journal.pone.0290750

    Article  Google Scholar 

  112. Xi E, Zhang J (2021) Research on image deblurring processing technology based on genetic algorithm. J Phys: Conf Ser 1852:022042. https://doi.org/10.1088/1742-6596/1852/2/022042

    Article  Google Scholar 

  113. Squires M, Tao X, Elangovan S et al (2022) A novel genetic algorithm based system for the scheduling of medical treatments. Expert Syst Appl 195:116464. https://doi.org/10.1016/j.eswa.2021.116464

    Article  Google Scholar 

  114. Liu C, Pan G, Song D, Wei H (2023) Air quality index forecasting via genetic algorithm-based improved extreme learning machine. IEEE Access 11:67086–67097. https://doi.org/10.1109/ACCESS.2023.3291146

    Article  Google Scholar 

  115. Mao T, Mihaita A-S, Chen F, Vu HL (2022) Boosted genetic algorithm using machine learning for traffic control optimization. IEEE Trans Intell Transp Syst 23:7112–7141. https://doi.org/10.1109/TITS.2021.3066958

    Article  Google Scholar 

  116. Khan AA, Abolhasan M, Ni W et al (2019) A hybrid-fuzzy logic guided genetic algorithm (H-FLGA) approach for resource optimization in 5G VANETs. IEEE Transp Veh Technol 68:6964–6974. https://doi.org/10.1109/TVT.2019.2915194

    Article  Google Scholar 

  117. Rath AK, Parhi DR, Das HC et al (2021) Design of a hybrid controller using genetic algorithm and neural network for path planning of a humanoid robot. Int J Intell Unman Syst 9:169–177. https://doi.org/10.1108/IJIUS-10-2019-0059

    Article  Google Scholar 

  118. Cáceres Flórez CA, Rosário JM, Amaya D (2020) Control structure for a car-like robot using artificial neural networks and genetic algorithms. Neural Comput Appl 32:15771–15784. https://doi.org/10.1007/s00521-018-3514-1

    Article  Google Scholar 

  119. Chen JL, Chang W-D (2009) Feedback linearization control of a two-link robot using a multi-crossover genetic algorithm. Expert Syst Appl 36:4154–4159. https://doi.org/10.1016/j.eswa.2008.01.048

    Article  Google Scholar 

  120. Veselý V, Osuský J, Sekaj I (2014) Gain scheduled controller design for thermo-optical plant. Arch Control Sci 24:333–349. https://doi.org/10.2478/acsc-2014-0020

    Article  MathSciNet  Google Scholar 

  121. Mukkapati ABK, Krishnasamy V, Kaur R (2020) Genetic algorithm assisted fixed frequency sliding mode controller for quadratic boost converter in fuel cell vehicle. IET Electr Syst Transp 10:81–88. https://doi.org/10.1049/iet-est.2019.0015

    Article  Google Scholar 

  122. Rodríguez-Abreo O, Garcia-Guendulain JM, Hernández-Alvarado R et al (2020) Genetic algorithm-based tuning of backstepping controller for a quadrotor-type unmanned aerial vehicle. Electronics 9:1735. https://doi.org/10.3390/electronics9101735

    Article  Google Scholar 

  123. Yang M, Li Y, Du H et al (2019) Hierarchical multiobjective h-infinity robust control design for wireless power transfer system using genetic algorithm. IEEE Trans Contr Syst Technol 27:1753–1761. https://doi.org/10.1109/TCST.2018.2814589

    Article  Google Scholar 

  124. Yasini T, Roshanian J, Taghavipour A (2023) Improving the low orbit satellite tracking ability using nonlinear model predictive controller and genetic algorithm. Adv Space Res 71:2723–2732. https://doi.org/10.1016/j.asr.2022.11.037

    Article  Google Scholar 

  125. Ramos Ruiz G, Lucas Segarra E, Fernández Bandera C (2018) Model predictive control optimization via genetic algorithm using a detailed building energy model. Energies 12:34. https://doi.org/10.3390/en12010034

    Article  Google Scholar 

  126. Dang X-K, Do V-D, Nguyen X-P (2020) Robust adaptive fuzzy control using genetic algorithm for dynamic positioning system. IEEE Access 8:222077–222092. https://doi.org/10.1109/ACCESS.2020.3043453

    Article  Google Scholar 

  127. Bhandari G, Raj R, Pathak PM, Yang J-M (2022) Robust control of a planar snake robot based on interval type-2 Takagi-Sugeno fuzzy control using genetic algorithm. Eng Appl Artif Intell 116:105437. https://doi.org/10.1016/j.engappai.2022.105437

    Article  Google Scholar 

  128. Pillai AG, Samuel ER, Unnikrishnan A (2019) Analysis of optimised LQR controller using genetic algorithm for isolated power system. In: Abraham A, Gandhi N, Pant M (eds) Innovations in bio-inspired computing and applications. Springer, Cham, pp 202–211

    Chapter  Google Scholar 

  129. Koch GG, Osorio CRD, Pinheiro H et al (2020) Design procedure combining linear matrix inequalities and genetic algorithm for robust control of grid-connected converters. IEEE Trans Ind Appl 56:1896–1906. https://doi.org/10.1109/TIA.2019.2959604

    Article  Google Scholar 

  130. Hanif O, Ranganayakulu R, Babu GUB, Kundu S (2023) Design of novel complex fractional order controller using genetic algorithm for fractional order system. In: Kumar J, Tripathy M, Jena P (eds) Control applications in modern power systems. Springer, Singapore, pp 77–87

    Chapter  Google Scholar 

  131. Wang H, Xu S, Hu H (2023) PID controller for PMSM speed control based on improved quantum genetic algorithm optimization. IEEE Access 11:61091–61102. https://doi.org/10.1109/ACCESS.2023.3284971

    Article  Google Scholar 

  132. Kaya İ, Nalbantoğlu M (2016) Simultaneous tuning of cascaded controller design using genetic algorithm. Electr Eng 98:299–305. https://doi.org/10.1007/s00202-016-0367-4

    Article  Google Scholar 

  133. Razali MR, Mohd Faudzi AA, Shamsudin AU, Mohamaddan S (2023) A hybrid controller method with genetic algorithm optimization to measure position and angular for mobile robot motion control. Front Robot AI 9:1087371. https://doi.org/10.3389/frobt.2022.1087371

    Article  Google Scholar 

  134. Ndiaye EHM, Ndiaye A, Faye M et al (2023) Chapter 12—adaptive neuro-fuzzy inference system and genetic algorithm (NFGA)-based MPPT controller for PV system: experimental realization. In: Fekik A, Ghanes M, Denoun H (eds) Power electronics converters and their control for renewable energy applications. Academic Press, New York, pp 265–282

    Chapter  Google Scholar 

  135. Pazooki M, Mazinan AH (2018) Hybrid fuzzy-based sliding-mode control approach, optimized by genetic algorithm for quadrotor unmanned aerial vehicles. Complex Intell Syst 4:79–93. https://doi.org/10.1007/s40747-017-0051-y

    Article  Google Scholar 

  136. Khosraviani M, Jahanshahi M, Farahani M, Bidaki ARZ (2018) Load-frequency control using multi-objective genetic algorithm and hybrid sliding mode control-based SMES. Int J Fuzzy Syst 20:280–294. https://doi.org/10.1007/s40815-017-0332-z

    Article  MathSciNet  Google Scholar 

  137. Kushwaha OS, Uthayakumar H, Kumaresan K (2022) Modeling of carbon dioxide fixation by microalgae using hybrid artificial intelligence (AI) and fuzzy logic (FL) methods and optimization by genetic algorithm (GA). Environ Sci Pollut Res 30:24927–24948. https://doi.org/10.1007/s11356-022-19683-0

    Article  Google Scholar 

  138. Habib M, Khoucha F, Harrag A (2017) GA-based robust LQR controller for interleaved boost DC–DC converter improving fuel cell voltage regulation. Electric Power Syst Res 152:438–456. https://doi.org/10.1016/j.epsr.2017.08.004

    Article  Google Scholar 

  139. Önen Ü, Çakan A, İLhan İ (2019) Performance comparison of optimization algorithms in LQR controller design fora nonlinear system. Turk J Elec Eng 27:1938–1953. https://doi.org/10.3906/elk-1808-51

    Article  Google Scholar 

  140. Carvalho L, Neto JRL, Rezende JC et al (2023) Linear quadratic regulator design via metaheuristics applied to the damping of low-frequency oscillations in power systems. ISA Trans 134:322–335. https://doi.org/10.1016/j.isatra.2022.08.024

    Article  Google Scholar 

  141. Nagarkar M, Vikhe Patil GJ (2016) Optimization of the linear quadratic regulator (LQR) control quarter car suspension system using genetic algorithm. ing.inv 36:23–30. https://doi.org/10.15446/ing.investig.v36n1.49253

  142. Ghoreishi SA, Nekoui MA (2012) Optimal weighting matrices design for LQR controller based on genetic algorithm and PSO. AMR 433–440:7546–7553. https://doi.org/10.4028/www.scientific.net/AMR.433-440.7546

    Article  Google Scholar 

  143. Abut T (2023) Optimal LQR controller methods for double inverted pendulum system on a cart. DÜMF MD 14:247–255. https://doi.org/10.24012/dumf.1253331

  144. Marada T, Matousek R, Zuth D (2017) Design of linear quadratic regulator (LQR) based on genetic algorithm for inverted pendulum. Mendel 23:149–156. https://doi.org/10.13164/mendel.2017.1.149

  145. Meng Y, Gan X, Wang Y, Gu Q (2019) LQR-GA controller for articulated dump truck path tracking system. J Shanghai Jiaotong Univ (Sci) 24:78–85. https://doi.org/10.1007/s12204-018-2012-z

    Article  Google Scholar 

  146. Gu J, Fang D (2021) Genetic algorithm based LQR control for AGV path tracking problem. J Phys 1952:032012. https://doi.org/10.1088/1742-6596/1952/3/032012

    Article  Google Scholar 

  147. Chen D, Zheng S, Wang H (2012) Genetic algorithm based LQR vibration wireless control of laminated plate using photostrictive actuators. Earthq Eng Eng Vib 11:83–90. https://doi.org/10.1007/s11803-012-0100-x

    Article  Google Scholar 

  148. Belyaev AS, Sumenkov OYu (2021) Hybrid control algorithm based on LQR and genetic algorithm for active support weight compensation system. IFAC-PapersOnLine 54:431–436. https://doi.org/10.1016/j.ifacol.2021.10.486

    Article  Google Scholar 

  149. Joelianto E, Christian D, Samsi A (2020) Swarm control of an unmanned quadrotor model with LQR weighting matrix optimization using genetic algorithm. J Mechatron Electr Power Veh Technol 11:1–10. https://doi.org/10.14203/j.mev.2020.v11.1-10

  150. Gupta S, Tripathi RK (2014) Optimal LQR controller in CSC based STATCOM using GA and PSO. Arch Electr Eng 63:469–487. https://doi.org/10.2478/aee-2014-0034

    Article  Google Scholar 

  151. Liang L, Yuan J, Zhang S, Zhao P (2018) Design a software real-time operation platform for wave piercing catamarans motion control using linear quadratic regulator based genetic algorithm. PLoS ONE 13:e0196107. https://doi.org/10.1371/journal.pone.0196107

    Article  Google Scholar 

  152. Mohammed IK, Abdulla AI (2020) Balancing a Segway robot using LQR controller based on genetic and bacteria foraging optimization algorithms. TELKOMNIKA 18:2642. https://doi.org/10.12928/telkomnika.v18i5.14717

  153. Ahmed JM (2020) Optimal tuning linear quadratic regulator for gas turbine by genetic algorithm using integral time absolute error. IJECE 10:1367. https://doi.org/10.11591/ijece.v10i2.pp1367-1375

  154. Abdullah AI, Alnema YHS, Thanoon MA (2022) Stabilization of three links inverted pendulum with cart based on genetic LQR approach. JESA 55:125–130. https://doi.org/10.18280/jesa.550113

  155. Nagarkar M, Bhalerao Y, Patil GV, Patil RZ (2018) Multi-objective optimization of nonlinear quarter car suspension system—PID and LQR control. Procedia Manuf 20:420–427. https://doi.org/10.1016/j.promfg.2018.02.061

    Article  Google Scholar 

  156. Ramirez C, Giral DA, Holguin M (2021) Linear quadratic regulator control with genetic algorithm convert applied to wind energy conversion. J Phys 2046:012024. https://doi.org/10.1088/1742-6596/2046/1/012024

    Article  Google Scholar 

  157. Nagarkar MP, Patil V (2016) Multi-objective optimization of LQR control quarter car suspension system using genetic algorithm. FME Trans 44:187–196. https://doi.org/10.5937/fmet1602187N

    Article  Google Scholar 

  158. Faris W, Kaleemullah M (2022) Optimisation of robust and LQR control parameters for discrete car model using genetic algorithm. IJVSMT 1:1. https://doi.org/10.1504/IJVSMT.2022.10049442

    Article  Google Scholar 

  159. Dhiman V, Singh G, Kumar M (2019) Modeling and control of underactuated system using LQR controller based on GA. In: Kumar M, Pandey RK, Kumar V (eds) Advances in interdisciplinary engineering. Springer, Singapore, pp 595–603

  160. Bendine K, Wankhade RL (2016) Vibration control of FGM piezoelectric plate based on LQR genetic search. Open J Civil Eng 06:1–7. https://doi.org/10.4236/ojce.2016.61001

    Article  Google Scholar 

  161. Bhushan R, Chatterjee K (2017) Mathematical modeling and control of DFIG-based wind energy system by using optimized linear quadratic regulator weight matrices. Int Trans Electr Energ Syst 27:e2416. https://doi.org/10.1002/etep.2416

    Article  Google Scholar 

  162. Shami TM, El-Saleh AA, Alswaitti M et al (2022) Particle swarm optimization: a comprehensive survey. IEEE Access 10:10031–10061. https://doi.org/10.1109/ACCESS.2022.3142859

    Article  Google Scholar 

  163. Minasian AA, Bird TS (2013) Particle swarm optimization of microstrip antennas for wireless communication systems. IEEE Trans Antennas Propagat 61:6214–6217. https://doi.org/10.1109/TAP.2013.2281517

    Article  Google Scholar 

  164. Li C, Yang S, Nguyen TT (2012) A self-learning particle swarm optimizer for global optimization problems. IEEE Trans Syst Man Cybern B 42:627–646. https://doi.org/10.1109/TSMCB.2011.2171946

    Article  Google Scholar 

  165. Luan F, Choi J-H, Jung H-K (2012) A particle swarm optimization algorithm with novel expected fitness evaluation for robust optimization problems. IEEE Trans Magn 48:331–334. https://doi.org/10.1109/TMAG.2011.2173753

    Article  Google Scholar 

  166. Tseng H-Y, Chu P-H, Lu H-C, Tsai M-J (2021) Easy particle swarm optimization for nonlinear constrained optimization problems. IEEE Access 9:124757–124767. https://doi.org/10.1109/ACCESS.2021.3110708

    Article  Google Scholar 

  167. Kassoul K, Zufferey N, Cheikhrouhou N, Brahim Belhaouari S (2022) Exponential particle swarm optimization for global optimization. IEEE Access 10:78320–78344. https://doi.org/10.1109/ACCESS.2022.3193396

    Article  Google Scholar 

  168. Rauf HT, Shoaib U, Lali MI et al (2020) Particle swarm optimization with probability sequence for global optimization. IEEE Access 8:110535–110549. https://doi.org/10.1109/ACCESS.2020.3002725

    Article  Google Scholar 

  169. Daamouche A, Melgani F, Alajlan N, Conci N (2013) Swarm optimization of structuring elements for VHR image classification. IEEE Geosci Remote Sensing Lett 10:1334–1338. https://doi.org/10.1109/LGRS.2013.2240649

    Article  Google Scholar 

  170. Zhang C, Zhou Q, Shuai B et al (2023) Dedicated adaptive particle swarm optimization algorithm for digital twin based control optimization of the plug-in hybrid vehicle. IEEE Trans Transp Electrific 9:3137–3148. https://doi.org/10.1109/TTE.2022.3219290

    Article  Google Scholar 

  171. Feng W, Zhang W, Huang S (2023) A novel parameter estimation method for PMSM by using chaotic particle swarm optimization with dynamic self-optimization. IEEE Trans Veh Technol 72:8424–8432. https://doi.org/10.1109/TVT.2023.3247729

    Article  Google Scholar 

  172. Zhang W, Zhang W (2022) An efficient UAV localization technique based on particle swarm optimization. IEEE Trans Veh Technol 71:9544–9557. https://doi.org/10.1109/TVT.2022.3178228

    Article  Google Scholar 

  173. AlRashidi MR, El-Hawary ME (2009) A survey of particle swarm optimization applications in electric power systems. IEEE Trans Evol Computat 13:913–918. https://doi.org/10.1109/TEVC.2006.880326

    Article  Google Scholar 

  174. Xu L, Zhang Z, Yao Y, Yu Z (2022) Improved particle swarm optimization-based BP neural networks for aero-optical imaging deviation prediction. IEEE Access 10:26769–26777. https://doi.org/10.1109/ACCESS.2021.3102669

    Article  Google Scholar 

  175. Zaini FA, Sulaima MF, Razak IAWA et al (2023) A review on the applications of PSO-based algorithm in demand side management: challenges and opportunities. IEEE Access 11:53373–53400. https://doi.org/10.1109/ACCESS.2023.3278261

    Article  Google Scholar 

  176. Mardani MM, Lazar RD, Mijatovic N, Dragičević T (2023) Artificial neural network-based constrained predictive real-time parameter adaptation controller for grid-tied VSCs. IEEE J Emerg Sel Topics Power Electron 11:1507–1517. https://doi.org/10.1109/JESTPE.2022.3214342

    Article  Google Scholar 

  177. Kou A, Li X (2023) Neural network intelligent control based on MPSO. IEEE Access 11:58565–58577. https://doi.org/10.1109/ACCESS.2023.3284969

    Article  Google Scholar 

  178. Dang X-K, Tran T-D, Do V-D et al (2022) Self-adaptive fuzzy control approach for jack-up rig jacking system based on particle swarm optimization. IEEE Access 10:86064–86077. https://doi.org/10.1109/ACCESS.2022.3197835

    Article  Google Scholar 

  179. Zhang L, Zheng H, Hu Q et al (2020) An adaptive droop control strategy for islanded microgrid based on improved particle swarm optimization. IEEE Access 8:3579–3593. https://doi.org/10.1109/ACCESS.2019.2960871

    Article  Google Scholar 

  180. Wang F, Li J, Li Z et al (2022) Design of model predictive control weighting factors for PMSM using gaussian distribution-based particle swarm optimization. IEEE Trans Ind Electron 69:10935–10946. https://doi.org/10.1109/TIE.2021.3120441

    Article  Google Scholar 

  181. Khan H, Abbasi SJ, Lee MC (2020) DPSO and inverse jacobian-based real-time inverse kinematics with trajectory tracking using integral SMC for teleoperation. IEEE Access 8:159622–159638. https://doi.org/10.1109/ACCESS.2020.3020318

    Article  Google Scholar 

  182. Chen C-C, Chen Y-T (2021) Feedback linearized optimal control design for quadrotor with multi-performances. IEEE Access 9:26674–26695. https://doi.org/10.1109/ACCESS.2021.3057378

    Article  Google Scholar 

  183. Safari A, Shayanfar HA, Kazemi A (2013) Robust PWMSC damping controller tuning on the augmented Lagrangian PSO algorithm. IEEE Trans Power Syst 28:4665–4673. https://doi.org/10.1109/TPWRS.2013.2271814

    Article  Google Scholar 

  184. Jia L, Zhao X (2019) An improved particle swarm optimization (PSO) optimized integral separation PID and its application on central position control system. IEEE Sensors J 19:7064–7071. https://doi.org/10.1109/JSEN.2019.2912849

    Article  Google Scholar 

  185. Assawinchaichote W, Angeli C, Pongfai J (2022) Proportional-integral-derivative parametric autotuning by novel stable particle swarm optimization (NSPSO). IEEE Access 10:40818–40828. https://doi.org/10.1109/ACCESS.2022.3167026

    Article  Google Scholar 

  186. Nan Y, Shao S, Ren C et al (2023) Simulation and experimental research on active suspension system with time-delay feedback control. IEEE Access 11:88498–88510. https://doi.org/10.1109/ACCESS.2023.3305265

    Article  Google Scholar 

  187. Zhang C-L, Wu X-Z, Xu J (2021) Particle swarm sliding mode-fuzzy PID control based on maglev system. IEEE Access 9:96337–96344. https://doi.org/10.1109/ACCESS.2021.3095490

    Article  Google Scholar 

  188. Zhao M, Zhao H, Zhao M (2023) Particle swarm optimization algorithm with adaptive two-population strategy. IEEE Access 11:62242–62260. https://doi.org/10.1109/ACCESS.2023.3287859

    Article  Google Scholar 

  189. Maghfiroh H, Nizam M, Anwar M, Ma’Arif A (2022) Improved LQR control using PSO optimization and kalman filter estimator. IEEE Access 10:18330–18337. https://doi.org/10.1109/ACCESS.2022.3149951

    Article  Google Scholar 

  190. Vinodh Kumar E, Raaja GS, Jerome J (2016) Adaptive PSO for optimal LQR tracking control of 2 DoF laboratory helicopter. Appl Soft Comput 41:77–90. https://doi.org/10.1016/j.asoc.2015.12.023

    Article  Google Scholar 

  191. Zhang Y, Li Y, Liu Y, Yi G (2020) Control of cricket system using LQR controller optimized by particle swarm optimization. J Phys 1670:012016. https://doi.org/10.1088/1742-6596/1670/1/012016

    Article  Google Scholar 

  192. Fang J (2014) The LQR controller design of two-wheeled self-balancing robot based on the particle swarm optimization algorithm. Math Probl Eng 2014:1–6. https://doi.org/10.1155/2014/729095

    Article  MathSciNet  Google Scholar 

  193. Kamil HG, Makki OT, Umran HM (2020) Optimal tuning of a linear quadratic regulator for position control using particle swarm optimisation. IOP Conf Ser 671:012047. https://doi.org/10.1088/1757-899X/671/1/012047

    Article  Google Scholar 

  194. Amini F, Hazaveh NK, Rad AA (2013) Wavelet PSO-based LQR algorithm for optimal structural control using active tuned mass dampers. Comput-Aided Civil Infrastruct Eng 28:542–557. https://doi.org/10.1111/mice.12017

    Article  Google Scholar 

  195. Zhang Y, Gao F, Zhao F (2023) Research on path planning and tracking control of autonomous vehicles based on improved RRT* and PSO-LQR. Processes 11:1841. https://doi.org/10.3390/pr11061841

    Article  Google Scholar 

  196. Dharavath PK, Ohri J (2021) Optimized control design of LQR for flexible joint manipulator. In: Vadhera S, Umre BS, Kalam A (eds) Latest trends in renewable energy technologies. Springer, Singapore, pp 261–269

  197. Ali N, Ayaz Y, Iqbal J (2022) Collaborative position control of pantograph robot using particle swarm optimization. Int J Control Autom Syst 20:198–207. https://doi.org/10.1007/s12555-019-0931-6

    Article  Google Scholar 

  198. Fang J, Li W (2019) Design of LQR controller based on particle swarm optimization algorithm for aircraft test simulation attitude control system. In: Abawajy J, Choo K-KR, Islam R, et al (eds) International conference on applications and techniques in cyber security and intelligence ATCI 2018. Springer, Cham, pp 1219–1226

  199. Duan H, Sun C (2013) Pendulum-like oscillation controller for micro aerial vehicle with ducted fan based on LQR and PSO. Sci China Technol Sci 56:423–429. https://doi.org/10.1007/s11431-012-5065-5

    Article  Google Scholar 

  200. Sreepradha AM, Rajan S (2021) Design and analysis of LQR controller using bees colony and particle swarm algorithm. Nat Volatiles Essent Oils 8:3242–3256

    Google Scholar 

  201. Wang M, Wang K, Zhao Q et al (2023) LQR control and optimization for trajectory tracking of biomimetic robotic fish based on unreal engine. Biomimetics 8:236. https://doi.org/10.3390/biomimetics8020236

    Article  Google Scholar 

  202. Gałecki A, Michalczuk M, Kaszewski A et al (2020) Grid-tied converter operated under unbalanced and distorted grid voltage conditions. Bull Pol Acad Sci Tech Sci 68:389–398. https://doi.org/10.24425/bpasts.2020.133109

  203. Ghosh A, Ray AK (2023) A gravitational search algorithm-based control of an underactuated system with experimental verifications. Soft Comput. https://doi.org/10.1007/s00500-023-08606-x

    Article  Google Scholar 

  204. Mobayen S (2011) Linear quadratic optimal control system design using particle swarm optimization algorithm. Int J Phys Sci. https://doi.org/10.5897/IJPS11.726

    Article  Google Scholar 

  205. Yang Y, Liu D (2023) A hybrid discrete artificial bee colony algorithm for imaging satellite mission planning. IEEE Access 11:40006–40017. https://doi.org/10.1109/ACCESS.2023.3269066

    Article  Google Scholar 

  206. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471. https://doi.org/10.1007/s10898-007-9149-x

    Article  MathSciNet  Google Scholar 

  207. Huang H-C, Chuang C-C (2020) Artificial bee colony optimization algorithm incorporated with fuzzy theory for real-time machine learning control of articulated robotic manipulators. IEEE Access 8:192481–192492. https://doi.org/10.1109/ACCESS.2020.3032715

    Article  Google Scholar 

  208. Yu Y, Zheng J, Chen S, Yang Z (2022) Moving target imaging via computational ghost imaging combined with artificial bee colony optimization. IEEE Trans Instrum Meas 71:1–7. https://doi.org/10.1109/TIM.2022.3156995

    Article  Google Scholar 

  209. Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8:687–697. https://doi.org/10.1016/j.asoc.2007.05.007

    Article  Google Scholar 

  210. Chen L, Wu T, Wang Z et al (2023) A novel hybrid BPNN model based on adaptive evolutionary Artificial Bee Colony Algorithm for water quality index prediction. Ecol Ind 146:109882. https://doi.org/10.1016/j.ecolind.2023.109882

    Article  Google Scholar 

  211. Watada J, Roy A, Wang B et al (2020) An artificial bee colony-based double layered neural network approach for solving quadratic bi-level programming problems. IEEE Access 8:21549–21564. https://doi.org/10.1109/ACCESS.2020.2967787

    Article  Google Scholar 

  212. Punitha S, Stephan T, Kannan R et al (2023) Detecting COVID-19 from lung computed tomography images: a swarm optimized artificial neural network approach. IEEE Access 11:12378–12393. https://doi.org/10.1109/ACCESS.2023.3236812

    Article  Google Scholar 

  213. Shah H (2021) Using new artificial bee colony as probabilistic neural network for breast cancer data classification. FEBE 1:133–145. https://doi.org/10.1108/FEBE-03-2021-0015

    Article  Google Scholar 

  214. Wang J, Liu Y, Rao S et al (2023) A novel self-adaptive multi-strategy artificial bee colony algorithm for coverage optimization in wireless sensor networks. Ad Hoc Netw 150:103284. https://doi.org/10.1016/j.adhoc.2023.103284

    Article  Google Scholar 

  215. Bai Y, Zhang C, Bai W (2023) A two-level parallel decomposition-based artificial bee colony method for dynamic multi-objective optimization problems. Appl Soft Comput. https://doi.org/10.1016/j.asoc.2023.110741

    Article  Google Scholar 

  216. Zhang S, Liu S (2015) A novel Artificial Bee Colony algorithm for function optimization. Math Probl Eng 2015:1–10. https://doi.org/10.1155/2015/129271

    Article  Google Scholar 

  217. Habib HUR, Wang S, Waqar A et al (2020) Combined heat and power units sizing and energy cost optimization of a residential building by using an Artificial Bee Colony algorithm. IEEE Access 8:218289–218303. https://doi.org/10.1109/ACCESS.2020.3042173

    Article  Google Scholar 

  218. Dong C, Xiong Z, Liu X et al (2019) Dual-search Artificial Bee Colony algorithm for engineering optimization. IEEE Access 7:24571–24584. https://doi.org/10.1109/ACCESS.2019.2899743

    Article  Google Scholar 

  219. Santhosh G, Prasad KV (2023) Energy optimization routing for hierarchical cluster based WSN using artificial bee colony. Measurement 29:100848. https://doi.org/10.1016/j.measen.2023.100848

    Article  Google Scholar 

  220. Zou W, Zhu Y, Chen H, Sui X (2010) A clustering approach using cooperative Artificial Bee Colony algorithm. Discret Dyn Nat Soc 2010:1–16. https://doi.org/10.1155/2010/459796

    Article  MathSciNet  Google Scholar 

  221. Karaboga D, Ozturk C (2011) A novel clustering approach: Artificial Bee Colony (ABC) algorithm. Appl Soft Comput 11:652–657. https://doi.org/10.1016/j.asoc.2009.12.025

    Article  Google Scholar 

  222. Al-Sawwa J, Almseidin M (2022) A spark-based Artificial Bee Colony algorithm for unbalanced large data classification. Information 13:530. https://doi.org/10.3390/info13110530

    Article  Google Scholar 

  223. Schiezaro M, Pedrini H (2013) Data feature selection based on Artificial Bee Colony algorithm. J Image Video Proc 2013:47. https://doi.org/10.1186/1687-5281-2013-47

    Article  Google Scholar 

  224. Rana M, Dahiya O, Singh P et al (2023) Grouped ABC for feature selection and mean-variance optimization for rule mining: a hybrid framework. IEEE Access 11:85747–85759. https://doi.org/10.1109/ACCESS.2023.3303360

    Article  Google Scholar 

  225. Wei B, Luo S, Yuan D (2023) Optimized combined forecasting model for hybrid signals in the displacement monitoring data of concrete dams. Structures 48:1989–2002. https://doi.org/10.1016/j.istruc.2023.01.096

    Article  Google Scholar 

  226. Kaya Keles M, Kilic U, Keles AE (2019) Proposed artificial bee colony algorithm as feature selector to predict the leadership perception of site managers. Comput J 64:408–417. https://doi.org/10.1093/comjnl/bxaa163

    Article  Google Scholar 

  227. Zhu S, Pun C-M, Zhu H et al (2023) An artificial bee colony algorithm with a balance strategy for wireless sensor network. Appl Soft Comput 136:110083. https://doi.org/10.1016/j.asoc.2023.110083

    Article  Google Scholar 

  228. Wang Z, Ding H, Li B et al (2020) An energy efficient routing protocol based on improved artificial bee colony algorithm for wireless sensor networks. IEEE Access 8:133577–133596. https://doi.org/10.1109/ACCESS.2020.3010313

    Article  Google Scholar 

  229. Han Y, Li G, Xu R et al (2020) Clustering the wireless sensor networks: a meta-heuristic approach. IEEE Access 8:214551–214564. https://doi.org/10.1109/ACCESS.2020.3041118

    Article  Google Scholar 

  230. Saad E, Elhosseini MA, Haikal AY (2019) Culture-based artificial bee colony with heritage mechanism for optimization of wireless sensors network. Appl Soft Comput 79:59–73. https://doi.org/10.1016/j.asoc.2019.03.040

    Article  Google Scholar 

  231. Hashim HA, Ayinde BO, Abido MA (2016) Optimal placement of relay nodes in wireless sensor network using artificial bee colony algorithm. J Netw Comput Appl 64:239–248. https://doi.org/10.1016/j.jnca.2015.09.013

    Article  Google Scholar 

  232. Li L, Sun L, Guo J et al (2017) A quick artificial bee colony algorithm for image thresholding. Information 8:16. https://doi.org/10.3390/info8010016

    Article  Google Scholar 

  233. Chen G, Zhang X, Wang ZJ, Li F (2015) An enhanced artificial bee colony-based support vector machine for image-based fault detection. Math Probl Eng 2015:1–12. https://doi.org/10.1155/2015/638926

    Article  Google Scholar 

  234. Gul E, Toprak AN (2023) Contourlet and discrete cosine transform based quality guaranteed robust image watermarking method using artificial bee colony algorithm. Expert Syst Appl 212:118730. https://doi.org/10.1016/j.eswa.2022.118730

    Article  Google Scholar 

  235. Chen J, Cai Z, Heidari AA et al (2023) Dynamic mechanism-assisted artificial bee colony optimization for image segmentation of COVID-19 chest X-ray. Displays 79:102485. https://doi.org/10.1016/j.displa.2023.102485

    Article  Google Scholar 

  236. Cuevas E, Sención-Echauri F, Zaldivar D, Pérez M (2013) Image segmentation using artificial bee colony optimization. In: Zelinka I, Snášel V, Abraham A (eds) Handbook of optimization: from classical to modern approach. Springer, Berlin, pp 965–990

    Chapter  Google Scholar 

  237. Pan X, Zhang Q, Pan H (2020) Improved artificial bee colony algorithm and its application to fundus retinal blood vessel image binarization. IEEE Access 8:123726–123734. https://doi.org/10.1109/ACCESS.2020.3001299

    Article  Google Scholar 

  238. Xu M, Zhang Y, Fan Y et al (2020) Linear spectral mixing model-guided artificial bee colony method for endmember generation. IEEE Geosci Remote Sensing Lett 17:2145–2149. https://doi.org/10.1109/LGRS.2019.2961502

    Article  Google Scholar 

  239. Öztürk Ş, Ahmad R, Akhtar N (2020) Variants of artificial bee colony algorithm and its applications in medical image processing. Appl Soft Comput 97:106799. https://doi.org/10.1016/j.asoc.2020.106799

    Article  Google Scholar 

  240. Ding X, Liu G, Du M et al (2016) Efficiency improvement of overall PMSM-inverter system based on artificial bee colony algorithm under full power range. IEEE Trans Magn 52:1–4. https://doi.org/10.1109/TMAG.2016.2526614

    Article  Google Scholar 

  241. Habib HUR, Subramaniam U, Waqar A et al (2020) Energy cost optimization of hybrid renewables based V2G microgrid considering multi objective function by using artificial bee colony optimization. IEEE Access 8:62076–62093. https://doi.org/10.1109/ACCESS.2020.2984537

    Article  Google Scholar 

  242. Gonzalez-Castano C, Restrepo C, Kouro S, Rodriguez J (2021) MPPT algorithm based on artificial bee colony for PV system. IEEE Access 9:43121–43133. https://doi.org/10.1109/ACCESS.2021.3066281

    Article  Google Scholar 

  243. Motahhir S, Chouder A, Hammoumi AE et al (2021) Optimal energy harvesting from a multistrings PV generator based on artificial bee colony algorithm. IEEE Syst J 15:4137–4144. https://doi.org/10.1109/JSYST.2020.2997744

    Article  Google Scholar 

  244. Hakli H (2023) The optimization of wind turbine placement using a binary artificial bee colony algorithm with multi-dimensional updates. Electric Power Syst Res 216:109094. https://doi.org/10.1016/j.epsr.2022.109094

    Article  Google Scholar 

  245. Debbah A, Kelaiaia R, Kerboua A (2023) A bee colony neuro-fuzzy controller to improve well premixed combustion. Strojnícky časopis 73:25–42. https://doi.org/10.2478/scjme-2023-0003

    Article  Google Scholar 

  246. Pattanaik V, Malika BK, Rout PK, Sahu BK (2023) Contingency-resilient PMU placement using fuzzy logic and discrete artificial bee colony algorithm for comprehensive network observability. Adv Electr Eng Electron Energy 5:100275. https://doi.org/10.1016/j.prime.2023.100275

  247. Kumar NK, Gopi RS, Kuppusamy R et al (2022) Fuzzy logic-based load frequency control in an island hybrid power system model using artificial bee colony optimization. Energies 15:2199. https://doi.org/10.3390/en15062199

    Article  Google Scholar 

  248. Chen C-H, Jeng S-Y, Lin C-J (2020) Using an adaptive fuzzy neural network based on a multi-strategy-based artificial bee colony for mobile robot control. Mathematics 8:1223. https://doi.org/10.3390/math8081223

    Article  Google Scholar 

  249. Padmanaban S, Priyadarshi N, Sagar Bhaskar M et al (2019) A hybrid ANFIS-ABC based MPPT controller for PV system with anti-islanding grid protection: experimental realization. IEEE Access 7:103377–103389. https://doi.org/10.1109/ACCESS.2019.2931547

    Article  Google Scholar 

  250. Ait Sahed O, Kara K, Benyoucef A, Hadjili ML (2016) An efficient artificial bee colony algorithm with application to nonlinear predictive control. Int J Gen Syst 45:393–417. https://doi.org/10.1080/03081079.2015.1086344

    Article  MathSciNet  Google Scholar 

  251. Bagheri A, Jabbari A, Mobayen S (2021) An intelligent ABC-based terminal sliding mode controller for load-frequency control of islanded micro-grids. Sustain Cities Soc 64:102544. https://doi.org/10.1016/j.scs.2020.102544

    Article  Google Scholar 

  252. Mughees A, Ahmad I (2023) Multi-optimization of novel conditioned adaptive barrier function integral terminal SMC for trajectory tracking of a quadcopter system. IEEE Access 11:88359–88377. https://doi.org/10.1109/ACCESS.2023.3304760

    Article  Google Scholar 

  253. Ramadan HS, Fathy A, Becherif M (2018) Optimal gain scheduling of VSC-HVDC system sliding mode control via artificial bee colony and mine blast algorithms. IET Gener Transm Distrib 12:661–669. https://doi.org/10.1049/iet-gtd.2017.0935

    Article  Google Scholar 

  254. Boureguig K, Soued S, Ouagueni F, Chahmi A (2023) Optimal metaheuristic-based feedback linearization control of DFIG wind turbine system. J Electr Eng Technol. https://doi.org/10.1007/s42835-023-01386-2

    Article  Google Scholar 

  255. Babaie M, Sharifzadeh M, Mehrasa M et al (2021) Supervised learning model predictive control trained by ABC algorithm for common-mode voltage suppression in NPC inverter. IEEE J Emerg Sel Topics Power Electron 9:3446–3456. https://doi.org/10.1109/JESTPE.2020.2984674

    Article  Google Scholar 

  256. Xu J, Tang H, Wang X et al (2022) NSGA-II algorithm-based LQG controller design for nuclear reactor power control. Ann Nucl Energy 169:108931. https://doi.org/10.1016/j.anucene.2021.108931

    Article  Google Scholar 

  257. Morar D, Dobra P (2021) Optimal LQR weight matrices selection for a CNC machine controller. In: 2021 23rd international conference on control systems and computer science (CSCS). IEEE, Bucharest, pp 21–26

  258. Du H, Liu P, Cui Q et al (2022) PID controller parameter optimized by reformative artificial bee colony algorithm. J Math 2022:1–16. https://doi.org/10.1155/2022/3826702

    Article  Google Scholar 

  259. Du H, Cui Q, Liu P et al (2022) PID controller enhanced with artificial bee colony algorithm for active magnetic bearing. Syst Sci Control Eng 10:686–697. https://doi.org/10.1080/21642583.2022.2102552

    Article  Google Scholar 

  260. Karaboga D, Akay B (2010) Proportional—integral—derivative controller design by using artificial bee colony, harmony search, and the bees algorithms. Proc Inst Mech Eng Part I 224:869–883. https://doi.org/10.1243/09596518JSCE954

    Article  Google Scholar 

  261. Acikgoz H, Yildiz C, Coteli R, Dandil B (2020) DC-link voltage control of three-phase PWM rectifier by using artificial bee colony based type-2 fuzzy neural network. Microprocess Microsyst 78:103250. https://doi.org/10.1016/j.micpro.2020.103250

    Article  Google Scholar 

  262. Abdul Zahra AK, Abdalla TY (2021) Design of fuzzy super twisting sliding mode control scheme for unknown full vehicle active suspension systems using an artificial bee colony optimization algorithm. Asian J Control 23:1966–1981. https://doi.org/10.1002/asjc.2352

    Article  Google Scholar 

  263. Gao H, Fu Z, Pun C-M et al (2022) An efficient artificial bee colony algorithm with an improved linkage identification method. IEEE Trans Cybern 52:4400–4414. https://doi.org/10.1109/TCYB.2020.3026716

    Article  Google Scholar 

  264. Ren X, Zhang H (2022) An improved artificial bee colony algorithm for model-free active noise control: algorithm and implementation. IEEE Trans Instrum Meas 71:1–11. https://doi.org/10.1109/TIM.2022.3196440

    Article  Google Scholar 

  265. Yao G, Wu Y, Huang X et al (2022) Clustering of typical wind power scenarios based on k-means clustering algorithm and improved artificial bee colony algorithm. IEEE Access 10:98752–98760. https://doi.org/10.1109/ACCESS.2022.3203695

    Article  Google Scholar 

  266. Thanoon MA, Awad SR, Abdullah IKh (2023) LQR controller design for stabilization of non-linear DIP system based on ABC algorithm. EEJET 2:36–44. https://doi.org/10.15587/1729-4061.2023.275657

  267. Wang H, Liao L, Wang D et al (2014) Improved artificial bee colony algorithm and its application in LQR controller optimization. Math Probl Eng 2014:1–8. https://doi.org/10.1155/2014/695637

    Article  Google Scholar 

  268. Tarczewski T, Niewiara LJ, Grzesiak LM (2020) Artificial bee colony based state feedback position controller for PMSM servo-drive—the efficiency analysis. Bull Pol Acad Sci Tech Sci 68:997–1007

    Google Scholar 

  269. Ata B, Coban R (2015) Artificial bee colony algorithm based linear quadratic optimal controller design for a nonlinear inverted pendulum. Int J Intell Syst Appl Eng 3:1–6

    Article  Google Scholar 

  270. Tarczewski T (2016) Application of artificial bee colony algorithm to auto-tuning of linear-quadratic regulator for PMSM position control. Electrotech Rev 1:59–64. https://doi.org/10.15199/48.2016.06.11

  271. IJEM (2018) Design of optimised linear quadratic regulator for capsule endoscopes based on artificial bee colony tuning algorithm. IJEM. https://doi.org/10.31534/engmod.2018.1-2.ri.02_vjan

  272. Changhao S, Duan H (2013) Artificial bee colony optimized controller for unmanned rotorcraft pendulum. Aircr Eng Aerosp Technol 85:104–114. https://doi.org/10.1108/00022661311302715

    Article  Google Scholar 

  273. Szczepanski R, Kaminski M, Tarczewski T (2020) Auto-tuning process of state feedback speed controller applied for two-mass system. Energies 13:3067. https://doi.org/10.3390/en13123067

    Article  Google Scholar 

  274. Tarczewski T, Grzesiak LM (2018) An application of novel nature-inspired optimization algorithms to auto-tuning state feedback speed controller for PMSM. IEEE Trans Ind Appl 54:2913–2925. https://doi.org/10.1109/TIA.2018.2805300

    Article  Google Scholar 

  275. Wang J-S, Li S-X (2019) An improved grey wolf optimizer based on differential evolution and elimination mechanism. Sci Rep 9:7181. https://doi.org/10.1038/s41598-019-43546-3

    Article  Google Scholar 

  276. Mohanty S, Subudhi B, Ray PK (2016) A new MPPT design using grey wolf optimization technique for photovoltaic system under partial shading conditions. IEEE Trans Sustain Energy 7:181–188. https://doi.org/10.1109/TSTE.2015.2482120

    Article  Google Scholar 

  277. Guo K, Cui L, Mao M et al (2020) An improved gray wolf optimizer MPPT algorithm for PV system with BFBIC converter under partial shading. IEEE Access 8:103476–103490. https://doi.org/10.1109/ACCESS.2020.2999311

    Article  Google Scholar 

  278. Reddy AKVK, Narayana KVL (2022) Symbiotic learning grey wolf optimizer for engineering and power flow optimization problems. IEEE Access 10:95229–95280. https://doi.org/10.1109/ACCESS.2022.3203999

    Article  Google Scholar 

  279. Liu J, Wei X, Huang H (2021) An improved grey wolf optimization algorithm and its application in path planning. IEEE Access 9:121944–121956. https://doi.org/10.1109/ACCESS.2021.3108973

    Article  Google Scholar 

  280. Zhang W, Zhang S, Wu F, Wang Y (2021) Path planning of UAV based on improved adaptive grey wolf optimization algorithm. IEEE Access 9:89400–89411. https://doi.org/10.1109/ACCESS.2021.3090776

    Article  Google Scholar 

  281. Li X, Luk KM (2020) The grey wolf optimizer and its applications in electromagnetics. IEEE Trans Antennas Propagat 68:2186–2197. https://doi.org/10.1109/TAP.2019.2938703

    Article  Google Scholar 

  282. Mahadeva R, Kumar M, Patole SP, Manik G (2022) Desalination plant performance prediction model using grey wolf optimizer based ANN approach. IEEE Access 10:34550–34561. https://doi.org/10.1109/ACCESS.2022.3162932

    Article  Google Scholar 

  283. Xu L, Wang H, Lin W et al (2019) GWO-BP neural network based op performance prediction for mobile multiuser communication networks. IEEE Access 7:152690–152700. https://doi.org/10.1109/ACCESS.2019.2948475

    Article  Google Scholar 

  284. Zhang X, Lu B, Zhang L et al (2023) An enhanced grey wolf optimizer boosted machine learning prediction model for patient-flow prediction. Comput Biol Med 163:107166. https://doi.org/10.1016/j.compbiomed.2023.107166

    Article  Google Scholar 

  285. Shahin I, Alomari OA, Nassif AB et al (2023) An efficient feature selection method for arabic and english speech emotion recognition using grey wolf optimizer. Appl Acoust 205:109279. https://doi.org/10.1016/j.apacoust.2023.109279

    Article  Google Scholar 

  286. Tukkee AS, Wahab NI, Mailah NF (2023) Optimal sizing of autonomous hybrid microgrids with economic analysis using grey wolf optimizer technique. Adv Electr Eng Electron Energy 3:100123

    Article  Google Scholar 

  287. Panguluri SK, Mohan L (2023) A novel fuzzy logic, gray wolf optimization and convolutional neural network based image fusion framework using discrete frame-let transform. Optik 273:170485. https://doi.org/10.1016/j.ijleo.2022.170485

    Article  Google Scholar 

  288. Sun Z, Cao Y, Wen Z et al (2023) A grey wolf optimizer algorithm based fuzzy logic power system stabilizer for single machine infinite bus system. Energy Rep 9:847–853. https://doi.org/10.1016/j.egyr.2023.04.365

    Article  Google Scholar 

  289. Zychlewicz M, Stanislawski R, Kaminski M (2022) Grey wolf optimizer in design process of the recurrent wavelet neural controller applied for two-mass system. Electronics 11:177. https://doi.org/10.3390/electronics11020177

    Article  Google Scholar 

  290. Bojan-Dragos C-A, Precup R-E, Petriu EM et al (2022) GWO-based optimal tuning of controllers for shape memory alloy wire actuators. IFAC-PapersOnLine 55:39–44. https://doi.org/10.1016/j.ifacol.2022.07.605

    Article  MathSciNet  Google Scholar 

  291. Tripathi S, Shrivastava A, Jana KC (2020) Self-tuning fuzzy controller for sun-tracker system using Gray Wolf Optimization (GWO) technique. ISA Trans 101:50–59. https://doi.org/10.1016/j.isatra.2020.01.012

    Article  Google Scholar 

  292. Wang B, Shahzad M, Zhu X et al (2020) A non-linear model predictive control based on grey-wolf optimization using least-square support vector machine for product concentration control in l-lysine fermentation. Sensors 20:3335. https://doi.org/10.3390/s20113335

    Article  Google Scholar 

  293. Daia Eddine OMC, Chebabhi A, Kessal A (2023) Backstepping based grey wolf and DPC for power quality improvement and active power injection in PV grid-connected system based on interleaved boost converter. Period Polytech Elec Eng Comp Sci 67:268–280. https://doi.org/10.3311/PPee.21852

    Article  Google Scholar 

  294. Vesović M, Jovanović R, Trišović N (2022) Control of a DC motor using feedback linearization and gray wolf optimization algorithm. Adv Mech Eng 14:168781322210853. https://doi.org/10.1177/16878132221085324

    Article  Google Scholar 

  295. Sekar K, Arasan E, Chandrasekaran K (2023) Grey wolf optimization and fed fast terminal sliding mode controllers based on interleaved boost converters for symmetric PV systems under asymmetric partial shading. Symmetry 15:1339. https://doi.org/10.3390/sym15071339

    Article  Google Scholar 

  296. Abhayadev S (2022) Optimum gain selection of sliding mode control using grey wolf optimization technique. In: 2022 second international conference on advances in electrical, computing, communication and sustainable technologies (ICAECT). IEEE, Bhilai, pp 1–6

  297. Qais MH, Hasanien HM, Alghuwainem S (2018) A grey wolf optimizer for optimum parameters of multiple PI controllers of a grid-connected PMSG driven by variable speed wind turbine. IEEE Access 6:44120–44128. https://doi.org/10.1109/ACCESS.2018.2864303

    Article  Google Scholar 

  298. Komathi C, Umamaheswari MG (2020) Design of gray wolf optimizer algorithm-based fractional order PI controller for power factor correction in SMPS applications. IEEE Trans Power Electron 35:2100–2118. https://doi.org/10.1109/TPEL.2019.2920971

    Article  Google Scholar 

  299. Dogruer T (2022) Grey wolf optimizer-based optimal controller tuning method for unstable cascade processes with time delay. Symmetry 15:54. https://doi.org/10.3390/sym15010054

    Article  Google Scholar 

  300. Nicola M, Nicola C-I (2021) Improved performance for PMSM control system based on LQR controller and computational intelligence. 2021 international conference on electrical, computer and energy technologies (ICECET). IEEE, Cape Town, pp 1–6

    Google Scholar 

  301. Faraj MA, Maalej B, Derbel N, Naifar O (2023) Adaptive fractional-order super-twisting sliding mode controller for lower limb rehabilitation exoskeleton in constraint circumstances based on the grey wolf optimization algorithm. Math Probl Eng 2023:1–32. https://doi.org/10.1155/2023/9641673

    Article  Google Scholar 

  302. Lal DK, Barisal AK, Tripathy M (2016) Grey wolf optimizer algorithm based fuzzy PID controller for AGC of multi-area power system with TCPS. Procedia Comput Sci 92:99–105. https://doi.org/10.1016/j.procs.2016.07.329

    Article  Google Scholar 

  303. Xiao L, Xu M, Chen Y, Chen Y (2019) Hybrid grey wolf optimization nonlinear model predictive control for aircraft engines based on an elastic BP neural network. Appl Sci 9:1254. https://doi.org/10.3390/app9061254

    Article  Google Scholar 

  304. Tu Q, Chen X, Liu X (2019) Hierarchy strengthened grey wolf optimizer for numerical optimization and feature selection. IEEE Access 7:78012–78028. https://doi.org/10.1109/ACCESS.2019.2921793

    Article  Google Scholar 

  305. Feng Y, Tang J, Su B et al (2020) Point cloud registration algorithm based on the grey wolf optimizer. IEEE Access 8:143375–143382. https://doi.org/10.1109/ACCESS.2020.3013706

    Article  Google Scholar 

  306. Erkol HO (2018) Linear quadratic regulator design for position control of an inverted pendulum by grey wolf optimizer. Ijacsa. https://doi.org/10.14569/IJACSA.2018.090403

  307. Razmjooy N, Ramezani M, Namadchian A (2016) A new LQR optimal control for a single-link flexible joint robot manipulator based on grey wolf optimizer. Majlesi J Electr Eng 10:53–60

    Google Scholar 

  308. Sun X, Hu C, Lei G et al (2020) State feedback control for a PM hub motor based on gray wolf optimization algorithm. IEEE Trans Power Electron 35:1136–1146. https://doi.org/10.1109/TPEL.2019.2923726

    Article  Google Scholar 

  309. Sun X, Wu M, Yang Z et al (2020) High-performance control for a permanent-magnet linear synchronous generator using state feedback control scheme plus grey wolf optimisation. IET Electr Power Appl 14:771–780. https://doi.org/10.1049/iet-epa.2019.0383

    Article  Google Scholar 

  310. Manna S, Mani G, Ghildiyal S et al (2022) Ant colony optimization tuned closed-loop optimal control intended for vehicle active suspension system. IEEE Access 10:53735–53745. https://doi.org/10.1109/ACCESS.2022.3164522

    Article  Google Scholar 

  311. David Reddipogu JS, Elumalai VK (2020) Hardware in the loop testing of adaptive inertia weight PSO-tuned LQR applied to vehicle suspension control. J Control Sci Eng 2020:1–16. https://doi.org/10.1155/2020/8873995

    Article  Google Scholar 

  312. Miyamoto K, She J, Sato D, Yasuo N (2018) Automatic determination of LQR weighting matrices for active structural control. Eng Struct 174:308–321. https://doi.org/10.1016/j.engstruct.2018.07.009

    Article  Google Scholar 

  313. Lahlouh I, Rerhrhaye F, Elakkary A et al (2023) Robust LQR control based on multidimensional particle swarm optimization for enhancing the dynamic performance of poultry house system. Int J Dynam Control 11:1593–1608. https://doi.org/10.1007/s40435-022-01082-5

    Article  Google Scholar 

  314. Wang L, Ni H, Zhou W et al (2014) MBPOA-based LQR controller and its application to the double-parallel inverted pendulum system. Eng Appl Artif Intell 36:262–268. https://doi.org/10.1016/j.engappai.2014.07.023

    Article  Google Scholar 

  315. Sun M, Ji C, Luan T, Wang N (2023) LQR pendulation reduction control of ship-mounted crane based on improved grey wolf optimization algorithm. Int J Precis Eng Manuf 24:395–407. https://doi.org/10.1007/s12541-022-00763-7

    Article  Google Scholar 

  316. Fan X, Wang J, Wang H et al (2023) LQR trajectory tracking control of unmanned wheeled tractor based on improved quantum genetic algorithm. Machines 11:62. https://doi.org/10.3390/machines11010062

    Article  Google Scholar 

  317. Cao Y, Li Y, Zhang G et al (2020) An efficient terminal voltage control for PEMFC based on an improved version of whale optimization algorithm. Energy Rep 6:530–542. https://doi.org/10.1016/j.egyr.2020.02.035

    Article  Google Scholar 

  318. Ismail HA, Packianather MS, Grosvenor RI (2017) Multi-objective invasive weed optimization of the LQR controller. Int J Autom Comput 14:321–339. https://doi.org/10.1007/s11633-017-1061-3

    Article  Google Scholar 

  319. Jokarzadeh M, Abedini M, Seifi A (2019) Improving power system damping using a combination of optimal control theory and differential evolution algorithm. ISA Trans 90:169–177. https://doi.org/10.1016/j.isatra.2018.12.039

    Article  Google Scholar 

  320. Pelz GM, Costa BLG, Da Silva SAO (2022) Tuning of state-feedback multi-resonant controllers based on LQR using differential evolution metaheuristic. Int J Electr Power Energy Syst 139:107965. https://doi.org/10.1016/j.ijepes.2022.107965

    Article  Google Scholar 

  321. Tijani SA, Mua’zu MB (2015) Stabilization of inverted pendulum system using intelligent linear quadratic regulator controller. In: 2015 7th international joint conference on computational intelligence (IJCCI). IEEE, Lisbon, pp 325–333

  322. Zhao W, Gu L, Dong M (2022) Application of artificial fish swarm algorithm in LQR control for active suspension. 2022 13th Asian control conference (ASCC). IEEE, Jeju, Korea, Republic of, pp 2406–2409

    Chapter  Google Scholar 

  323. Das RR, Elumalai VK, Ganapathy Subramanian R, Ashok Kumar KV (2018) Adaptive predator–prey optimization for tuning of infinite horizon LQR applied to vehicle suspension system. Appl Soft Comput 72:518–526. https://doi.org/10.1016/j.asoc.2018.06.044

    Article  Google Scholar 

  324. Chen P-C, Sugiarto BJ, Chien K-Y (2021) Performance-based optimization of LQR for active mass damper using symbiotic organisms search. Smart Struct Syst 27:705–717. https://doi.org/10.12989/SSS.2021.27.4.705

  325. Bilgic HH, Sen MA, Kalyoncu M (2016) Tuning of LQR controller for an experimental inverted pendulum system based on the Bees Algorithm. J Vibroeng 18:3684–3694. https://doi.org/10.21595/jve.2016.16787

  326. Bilgic HH, Sen MA, Yapici A et al (2021) Meta-heuristic tuning of the LQR weighting matrices using various objective functions on an experimental flexible arm under the effects of disturbance. Arab J Sci Eng 46:7323–7336. https://doi.org/10.1007/s13369-021-05428-7

    Article  Google Scholar 

  327. Hassani K, Lee W-S (2016) Multi-objective design of state feedback controllers using reinforced quantum-behaved particle swarm optimization. Appl Soft Comput 41:66–76. https://doi.org/10.1016/j.asoc.2015.12.024

    Article  Google Scholar 

  328. Komarudin A, Setyawan N, Kamajaya L, et al (2021) Signature PSO: a novel inertia weight adjustment using fuzzy signature for LQR tuning. Bull EEI 10:308–318. https://doi.org/10.11591/eei.v10i1.2667

  329. Abdillah M, Setiadi H, Reihara AB et al (2016) Optimal selection of LQR parameter using AIS for LFC in a multi-area power system. J Mechatron Electr Power Veh Technol 7:93–104

    Article  Google Scholar 

  330. Attia M, Bechouat M, Sedraoui M, Aoulmi Z (2022) An optimal linear quadratic regulator in closed loop with boost converter for current photovoltaic application. Eur J Electr Eng 24:97–103

    Article  Google Scholar 

  331. Li C, Shen L, Shao J, Fang J (2023) Simulation and experiment of active vibration control based on flexible piezoelectric MFC composed of PZT and PI layer. Polymers 15:1819. https://doi.org/10.3390/polym15081819

    Article  Google Scholar 

  332. El-Naggar A, Korai A, Erlich I (2015) Using MVMO for optimal tuning of linear quadratic regulators for DFIG-WT. IFAC-PapersOnLine 48:479–484. https://doi.org/10.1016/j.ifacol.2015.12.425

    Article  Google Scholar 

  333. Panjwani B, Kumar V, Yadav J, Mohan V (2023) Optimum LQR controller for inverted pendulum using whale optimization algorithm. In: Rani A, Kumar B, Shrivastava V, Bansal RC (eds) Signals, machines and automation. Springer, Singapore, pp 307–315

  334. Herlambang T, Rahmalia D, Nurhadi H et al (2020) Optimization of linear quadratic regulator with tracking applied to autonomous underwater vehicle (AUV) using cuckoo search. Nonlinear Dyn Syst Theory 20:282–298

    MathSciNet  Google Scholar 

  335. Chi X, Chi R (2020) Optimal design of linear quadratic regulator controller based on adaptive cuckoo search algorithm. In: 2020 7th international conference on information science and control engineering (ICISCE). IEEE, Changsha, pp 1981–1986

  336. Meng J, Chen Q, He R (2014) Research on optimal control for the vehicle suspension based on the simulated annealing algorithm. J Appl Math 2014:1–5. https://doi.org/10.1155/2014/420719

    Article  Google Scholar 

  337. Radaideh A, Bodoor M, Al-Quraan A (2021) Active and reactive power control for wind turbines based DFIG using LQR controller with optimal gain-scheduling. J Electr Comput Eng 2021:1–19. https://doi.org/10.1155/2021/1218236

    Article  Google Scholar 

  338. Kumar V, Sharma V, Naresh R, Kumar V (2022) MVO-optimized linear quadratic regulator for automatic voltage controller system. In: Mandal JK, Hsiung P-A, Sankar Dhar R (eds) Topical drifts in intelligent computing. Springer, Singapore, pp 573–580

  339. Abdullah H (2021) An improvement in LQR controller design based on modified chaotic particle swarm optimization and model order reduction. IJIES 14:157–168. https://doi.org/10.22266/ijies2021.0228.16

  340. Zeng X, Zhang J, Li H (2021) Application of the hybrid genetic particle swarm algorithm to design the linear quadratic regulator controller for the accelerator power supply. Radiat Detect Technol Methods 5:128–135. https://doi.org/10.1007/s41605-021-00248-7

    Article  Google Scholar 

  341. Blondin MJ, Pardalos PM (2020) A holistic optimization approach for inverted cart-pendulum control tuning. Soft Comput 24:4343–4359. https://doi.org/10.1007/s00500-019-04198-7

    Article  Google Scholar 

  342. Zhao W, Gu L (2023) Hybrid particle swarm optimization genetic LQR controller for active suspension. Appl Sci 13:8204. https://doi.org/10.3390/app13148204

    Article  Google Scholar 

  343. Pillai AG, Rita Samuel E (2021) PSO based LQR-PID output feedback for load frequency control of reduced power system model using balanced truncation. Int Trans Electr Energy Syst 31:e13012. https://doi.org/10.1002/2050-7038.13012

    Article  Google Scholar 

  344. Abdul Samad B, Mohamed M, Anayi F (2023) Enhanced the control strategy of a triple link robotic system (robogymnast). IEEE Access 11:31997–32005. https://doi.org/10.1109/ACCESS.2023.3262190

    Article  Google Scholar 

  345. Mohammed IK, Abdulla AI (2020) Elevation, pitch and travel axis stabilization of 3DOF helicopter with hybrid control system by GA-LQR based PID controller. IJECE 10:1868

    Article  Google Scholar 

  346. Calgan H, Demirtas M (2021) A robust LQR-FOPIλDµ controller design for output voltage regulation of stand-alone self-excited induction generator. Electric Power Syst Res 196:107175. https://doi.org/10.1016/j.epsr.2021.107175

    Article  Google Scholar 

  347. Shauqee MN, Rajendran P, Suhadis NM (2021) Proportional double derivative linear quadratic regulator controller using improvised grey wolf optimization technique to control quadcopter. Appl Sci 11:2699. https://doi.org/10.3390/app11062699

    Article  Google Scholar 

  348. Son NN, Kien CV, Anh HPH (2019) Uncertain nonlinear system control using hybrid fuzzy LQR-sliding mode technique optimized with evolutionary algorithm. Eng Comput 36:1893–1912. https://doi.org/10.1108/EC-08-2018-0356

    Article  Google Scholar 

  349. Sen MA, Kalyoncu M (2019) Grey wolf optimizer based tuning of a hybrid LQR-PID controller for foot trajectory control of a quadruped robot. GU J Sci 32:674–684

    Google Scholar 

  350. Hussein R (2023) Design a new hybrid controller based on an improvement version of grey wolf optimization for trajectory tracking of wheeled mobile robot. FME Trans 51:140–148. https://doi.org/10.5937/fme2302140H

    Article  Google Scholar 

  351. Ebrahim MA, Mousa ME, Said EM et al (2020) Optimal design of hybrid optimization technique for balancing inverted pendulum system. Wseas Trans Syst 19:138–148

    Article  Google Scholar 

  352. Artale V, Milazzo CLR, Orlando C, Ricciardello A (2015) Genetic algorithm applied to the stabilization control of a hexarotor. AIP Conf Proc 1648:780003. https://doi.org/10.1063/1.4912983

    Article  Google Scholar 

  353. Heidari AH, Etedali S, Javaheri-Tafti MR (2018) A hybrid LQR-PID control design for seismic control of buildings equipped with ATMD. Front Struct Civ Eng 12:44–57. https://doi.org/10.1007/s11709-016-0382-6

    Article  Google Scholar 

  354. Abut T, Salkim E (2023) Control of quarter-car active suspension system based on optimized fuzzy linear quadratic regulator control method. Appl Sci 13:8802. https://doi.org/10.3390/app13158802

    Article  Google Scholar 

  355. Choubey C, Ohri J (2022) Tuning of LQR-PID controller to control parallel manipulator. Neural Comput Appl 34:3283–3297. https://doi.org/10.1007/s00521-021-06608-0

    Article  Google Scholar 

  356. Huang Y, Luo W, Huang D, Lan H (2023) Cascade optimization control of unmanned vehicle path tracking under harsh driving conditions. J Shanghai Jiaotong Univ (Sci) 28:114–125. https://doi.org/10.1007/s12204-023-2574-2

    Article  Google Scholar 

  357. Bekkar B, Ferkous K (2023) Design of online fuzzy tuning LQR controller applied to rotary single inverted pendulum: experimental validation. Arab J Sci Eng 48:6957–6972. https://doi.org/10.1007/s13369-022-06921-3

    Article  Google Scholar 

  358. Ghiloubi IB, Abdou L, Lahmar O (2023) PD-LQR control of 3DOF helicopter using FPA optimization. In: 2023 international conference on control, automation and diagnosis (ICCAD). IEEE, Rome, pp 1–6

  359. Choubey C, Ohri J (2023) GWO-based tuning of LQR-PID controller for a 3-DOF parallel manipulator. IETE J Res 69:4378–4393. https://doi.org/10.1080/03772063.2021.1958068

    Article  Google Scholar 

  360. Rahman ZA, Mat Isa AA, Ali HH, Anuar MA (2013) Control of flexible beam with unmodelled dynamics using second-order pole placement and LQR techniques. AMM 393:675–682. https://doi.org/10.4028/www.scientific.net/AMM.393.675

    Article  Google Scholar 

  361. Baroudi M, Saad M, Ghie W, et al (2010) Vibration controllability and observability of a single-link flexible manipulator. In: 2010 7th international multi- conference on systems, signals and devices. IEEE, Amman, Jordan, pp 1–6

  362. Barrera-Cardenas R, Molinas M (2012) Optimal LQG controller for variable speed wind turbine based on genetic algorithms. Energy Procedia 20:207–216. https://doi.org/10.1016/j.egypro.2012.03.021

    Article  Google Scholar 

  363. Workeye EA, G, Meskel TG, T, Himanot YK, (2022) Design of genetic algorithm based robust LQG controller for active magnetic bearing system. In: Berihun ML (ed) Advances of science and technology. Springer, Cham, pp 215–236

    Chapter  Google Scholar 

  364. Abdulla I, Mohammed IK (2023) Aircraft pitch control design using LQG controller based on genetic algorithm. TELKOMNIKA 21:409. https://doi.org/10.12928/telkomnika.v21i2.22051

  365. Gibson J, Hadi MU (2022) Modeling and optimal control for rotary unmanned aerial vehicles in northern Ireland climate. Appl Sci 12:7677. https://doi.org/10.3390/app12157677

    Article  Google Scholar 

  366. Likaj R, Shala A (2018) Optimisation and control of vehicle suspension using linear quadratic Gaussian control. Strojnícky casopis 68:61–68. https://doi.org/10.2478/scjme-2018-0006

    Article  Google Scholar 

  367. Pang H, Chen Y, Chen J, Liu X (2017) Design of LQG controller for active suspension without considering road input signals. Shock Vib 2017:1–13. https://doi.org/10.1155/2017/6573567

    Article  Google Scholar 

  368. Mei TX, Goodall RM (2000) LQG and GA solutions for active steering of railway vehicles. IEE Proc 147:111–117. https://doi.org/10.1049/ip-cta:20000145

    Article  Google Scholar 

  369. Choubey C, Ohri J (2018) Parallel manipulator control using different LQG tuning methods. In: 2018 5th IEEE Uttar Pradesh section international conference on electrical, electronics and computer engineering (UPCON). IEEE, Gorakhpur, pp 1–6

  370. Roni MdHK, Emal YEH, Solayman S et al (2022) Optimizing LQG controller for a single-phase power inverter in an AC microgrid system. In: 2022 4th international conference on sustainable technologies for industry 4.0 (STI). IEEE, Dhaka, pp 1–5

  371. Roni MdHK, Rana MS (2021) Data-driven linear quadratic control scheme for three-phase microgrid system optimized by genetic algorithm. In: 2021 International conference on emerging smart computing and informatics (ESCI). IEEE, Pune, India, pp 549–554

  372. Rodríguez-Barrera JA, Parra-Raad JA, Roa-Prada S (2014) Parameter optimization of a linear-quadratic-Gaussian controller for a proton exchange membrane fuel cell using genetic algorithms. In: Dynamics, vibration, and control, vol 4A. American Society of Mechanical Engineers, Montreal, p V04AT04A010

  373. Mohammed IK, Noaman MN (2022) Optimal control approach for robot system using LQG technique. J Eur Syst Autom 55:671–677

    Google Scholar 

  374. Fessi R, Bouallègue S (2019) LQG controller design for a quadrotor UAV based on particle swarm optimisation. Int J Autom Control 13:569–594

    Article  Google Scholar 

  375. Remes CL, Rosa MB, Heerdt JA, Oliveira SVG (2021) LQG controller in cascade loop tuned by PSO applied to a DC–DC converter. Asian J Control 23:2370–2380. https://doi.org/10.1002/asjc.2373

    Article  Google Scholar 

  376. Geetha M, Sivaraman N, Sanjeevikumar P (2018) Particle swarm optimization-based closed-loop optimal state feedback control for CSTR. In: Konkani A, Bera R, Paul S (eds) Advances in systems, control and automation. Springer, Singapore, pp 469–479

  377. Li B, Sinha U, Sankaranarayanan G (2016) Modelling and control of non-linear tissue compression and heating using an LQG controller for automation in robotic surgery. Trans Inst Meas Control 38:1491–1499. https://doi.org/10.1177/0142331215596062

    Article  Google Scholar 

  378. Hosseinian PS, Ebrahimi S, Jatskevich J (2021) An optimization-based load frequency control in an interconnected multi-area power system using linear quadratic Gaussian tuned via PSO. In: 2021 IEEE electrical power and energy conference (EPEC). IEEE, Toronto, ON, pp 119–124

  379. Wang W, Jing Y, Yang L et al (2012) Weight optimization for LQG controller based on the artificial bee colony algorithm. AASRI Procedia 3:686–693. https://doi.org/10.1016/j.aasri.2012.11.109

    Article  Google Scholar 

  380. Ma R, Wu H, Ding L (2017) Artificial bee colony optimised controller for small-scale unmanned helicopter. Aeronaut J 121:1879–1896. https://doi.org/10.1017/aer.2017.106

    Article  Google Scholar 

  381. Ma R, Ding L, Wu H (2018) Dynamic decoupling control optimization for a small-scale unmanned helicopter. J Robot 2018:1–12. https://doi.org/10.1155/2018/9897684

    Article  Google Scholar 

  382. Rakhshani E, Naveh IMH, Mehrjerdi H, Pan K (2021) An optimized LQG servo controller design using LQI tracker for VSP-based AC/DC interconnected systems. Int J Electr Power Energy Syst 129:106752. https://doi.org/10.1016/j.ijepes.2020.106752

    Article  Google Scholar 

  383. Zeng W, Li J, Hui T et al (2020) LQG/LTR controller with simulated annealing algorithm for CIADS core power control. Ann Nucl Energy 142:107422. https://doi.org/10.1016/j.anucene.2020.107422

    Article  Google Scholar 

  384. Hasan MW, Abbas NH (2021) Controller design for underwater robotic vehicle based on improved whale optimization algorithm. Bull Electr Eng Inform 10:609–618. https://doi.org/10.11591/eei.v10i2.2288

  385. Kumar L, Kumar P, Dhillon SS (2020) A multiobjective optimization approach for linear quadratic Gaussian/loop transfer recovery design. Optim Control Appl Methods 41:1267–1287. https://doi.org/10.1002/oca.2603

    Article  MathSciNet  Google Scholar 

  386. Benkhoud K, Bouallègue S (2018) Dynamics modeling and advanced metaheuristics based LQG controller design for a Quad Tilt Wing UAV. Int J Dynam Control 6:630–651. https://doi.org/10.1007/s40435-017-0325-7

    Article  MathSciNet  Google Scholar 

  387. Liu W, Hu Z, Wang J, Liu S (2020) A self-tuning controller design method based on LQG/LTR and back propagation algorithm. In: Jia Y, Du J, Zhang W (eds) Proceedings of 2019 Chinese intelligent systems conference. Springer, Singapore, pp 254–259

  388. Zhang M, Sun P, Cao R, Zhu J (2010) LQG/LTR flight controller optimal design based on differential evolution algorithm. In: 2010 international conference on intelligent computation technology and automation. IEEE, Changsha, pp 613–616

  389. Li F, Luo S, Zhang S, Xiao K (2021) LQG control of vehicle active suspension using whale optimization algorithm. In: 2021 China automation congress (CAC). IEEE, Beijing, pp 8306–8309

  390. Ma F, Wang J, Wang Y, Yang L (2018) Optimization design of semi-active controller for in-wheel motors suspension. J Vibroeng 20:2908–2924

    Article  Google Scholar 

  391. Lin X, Lin W (2022) Whale optimization algorithm-based LQG-adaptive neuro-fuzzy control for seismic vibration mitigation with MR dampers. Shock Vib 2022:1–21. https://doi.org/10.1155/2022/4060660

    Article  Google Scholar 

  392. Khamies M, Magdy G, Kamel S, Khan B (2021) Optimal model predictive and linear quadratic Gaussian control for frequency stability of power systems considering wind energy. IEEE Access 9:116453–116474. https://doi.org/10.1109/ACCESS.2021.3106448

    Article  Google Scholar 

  393. Khamies M, Magdy G, Hussein ME et al (2020) An efficient control strategy for enhancing frequency stability of multi-area power system considering high wind energy penetration. IEEE Access 8:140062–140078. https://doi.org/10.1109/ACCESS.2020.3012119

    Article  Google Scholar 

  394. Ghouraf DE, Naceri A (2017) Robust H2-PSS design based on LQG control optimized by genetic algorithms. Aut Control Comp Sci 51:301–310. https://doi.org/10.3103/S0146411617050030

    Article  Google Scholar 

  395. Mishra S, Patel S, Prusty RC, Panda S (2020) MVO optimized hybrid FOFPID-LQG controller for load frequency control of an AC micro-grid system. World J Eng 17:675–686. https://doi.org/10.1108/WJE-05-2019-0142

    Article  Google Scholar 

  396. Das S, Halder K (2014) Missile attitude control via a hybrid LQG-LTR-LQI control scheme with optimum weight selection. 2014 first international conference on automation, control, energy and systems (ACES). IEEE, India, pp 1–6

    Google Scholar 

  397. Khamies M, Magdy G, Ebeed M, Kamel S (2021) A robust PID controller based on linear quadratic Gaussian approach for improving frequency stability of power systems considering renewables. ISA Trans 117:118–138. https://doi.org/10.1016/j.isatra.2021.01.052

    Article  Google Scholar 

  398. Ensermu G, Vijayashanthi M, Suresh M et al (2023) An FRLQG controller-based small-signal stability enhancement of hybrid microgrid using the BCSSO algorithm. J Electr Comput Eng 2023:1–15. https://doi.org/10.1155/2023/8404457

    Article  Google Scholar 

  399. Mishra S, Nayak PC, Prusty UC, Prusty RC (2020) Secondary load frequency control of an islanded microgrid by SSA optimized hybrid PID-LQG controller. In: 2020 international conference on renewable energy integration into smart grids: a multidisciplinary approach to technology modelling and simulation (ICREISG). IEEE, Bhubaneswar, pp 153–157

  400. Waszak M, Langowski R (2020) An automatic self-tuning control system design for an inverted pendulum. IEEE Access 8:26726–26738. https://doi.org/10.1109/ACCESS.2020.2971788

    Article  Google Scholar 

  401. Valluru SK, Singh M (2017) Stabilization of nonlinear inverted pendulum system using MOGA and APSO tuned nonlinear PID controller. Cogent Eng 4:1357314. https://doi.org/10.1080/23311916.2017.1357314

    Article  Google Scholar 

  402. Zeghlache S, Ghellab MZ, Djerioui A et al (2023) Adaptive fuzzy fast terminal sliding mode control for inverted pendulum-cart system with actuator faults. Math Comput Simul 210:207–234. https://doi.org/10.1016/j.matcom.2023.03.005

    Article  MathSciNet  Google Scholar 

  403. Dörfler F, Bullo F (2014) Synchronization in complex networks of phase oscillators: a survey. Automatica 50:1539–1564. https://doi.org/10.1016/j.automatica.2014.04.012

    Article  MathSciNet  Google Scholar 

  404. Ramos J, Kim S (2018) Dynamic bilateral teleoperation of the cart-pole: a study toward the synchronization of human operator and legged robot. IEEE Robot Autom Lett 3:3293–3299. https://doi.org/10.1109/LRA.2018.2852840

    Article  Google Scholar 

  405. Dai F, Gao X, Jiang S et al (2015) A two-wheeled inverted pendulum robot with friction compensation. Mechatronics 30:116–125. https://doi.org/10.1016/j.mechatronics.2015.06.011

    Article  Google Scholar 

  406. Zhang Y, Zhang L, Wang W et al (2018) Design and implementation of a two-wheel and hopping robot with a linkage mechanism. IEEE Access 6:42422–42430. https://doi.org/10.1109/ACCESS.2018.2859840

    Article  Google Scholar 

  407. Velazquez M, Cruz D, Garcia S, Bandala M (2016) Velocity and motion control of a self-balancing vehicle based on a cascade control strategy. Int J Adv Rob Syst 13:106. https://doi.org/10.5772/63933

    Article  Google Scholar 

  408. Sambo AU, Bala FS, Tahir NM, Babawuro AY (2020) Optimal control of inverted pendulum on cart system. J Phys 1502:012024. https://doi.org/10.1088/1742-6596/1502/1/012024

    Article  Google Scholar 

  409. Messikh L, Guechi E-H, Bourahala F, Blažič S (2022) Stabilization of the cart-inverted-pendulum system using trivial state-feedback to output-feedback control conversion. Automatika 63:640–655. https://doi.org/10.1080/00051144.2022.2059950

    Article  Google Scholar 

  410. Krishnan A, U PKrishna, Bukya M, et al (2021) A comparative study on intelligent & adaptive control techniques on a nonlinear inverted pendulum cart mechanism. In: 2021 9th international conference on reliability, infocom technologies and optimization (trends and future directions) (ICRITO). IEEE, Noida, pp 1–6

  411. Llama M, Flores A, Garcia-Hernandez R, Santibañez V (2020) Heuristic global optimization of an adaptive fuzzy controller for the inverted pendulum system: experimental comparison. Appl Sci 10:6158. https://doi.org/10.3390/app10186158

    Article  Google Scholar 

  412. Israilov S, Fu L, Sánchez-Rodríguez J et al (2023) Reinforcement learning approach to control an inverted pendulum: a general framework for educational purposes. PLoS ONE 18:e0280071. https://doi.org/10.1371/journal.pone.0280071

    Article  Google Scholar 

  413. Prasad LB, Gupta HO, Tyagi B (2014) Adaptive optimal control of nonlinear inverted pendulum system using policy iteration technique. IFAC Proc Vol 47:1138–1145. https://doi.org/10.3182/20140313-3-IN-3024.00144

    Article  Google Scholar 

  414. Adhikary N, Mahanta C (2013) Integral backstepping sliding mode control for underactuated systems: swing-up and stabilization of the Cart-Pendulum system. ISA Trans 52:870–880. https://doi.org/10.1016/j.isatra.2013.07.012

    Article  Google Scholar 

  415. Pramanik S, Anwar S (2022) Robust controller design for rotary inverted pendulum using H-infinity and mu-synthesis techniques. J Eng 2022:249–260. https://doi.org/10.1049/tje2.12078

    Article  Google Scholar 

  416. Messikh L, ElH G, Benloucif ML (2017) Critically damped stabilization of inverted-pendulum systems using continuous-time cascade linear model predictive control. J Franklin Inst 354:7241–7265. https://doi.org/10.1016/j.jfranklin.2017.08.039

    Article  MathSciNet  Google Scholar 

  417. Prasad LB, Tyagi B, Gupta HO (2014) Optimal control of nonlinear inverted pendulum system using PID controller and LQR: performance analysis without and with disturbance input. Int J Autom Comput 11:661–670. https://doi.org/10.1007/s11633-014-0818-1

    Article  Google Scholar 

  418. Mishra SK, Chandra D (2014) Stabilization and tracking control of inverted pendulum using fractional order PID controllers. J Eng 2014:1–9. https://doi.org/10.1155/2014/752918

    Article  Google Scholar 

  419. Jafary Fesharaki A, Tabatabaei M (2022) Adaptive hierarchical fractional-order sliding mode control of an inverted pendulum-cart system. Arab J Sci Eng 47:13927–13942. https://doi.org/10.1007/s13369-022-06613-y

    Article  Google Scholar 

  420. Jung S, Kim SS (2007) Hardware implementation of a real-time neural network controller with a DSP and an FPGA for nonlinear systems. IEEE Trans Ind Electron 54:265–271. https://doi.org/10.1109/TIE.2006.888791

    Article  Google Scholar 

  421. Kumar V, Agarwal R (2022) Modeling and control of inverted pendulum cart system using PID-LQR based modern controller. In: 2022 IEEE students conference on engineering and systems (SCES). IEEE, Prayagraj, pp 01–05

  422. Onen U (2023) Model-free controller design for nonlinear underactuated systems with uncertainties and disturbances by using extended state observer based chattering-free sliding mode control. IEEE Access 11:2875–2885. https://doi.org/10.1109/ACCESS.2023.3234864

    Article  Google Scholar 

  423. Gao H, Li X, Gao C, Wu J (2021) Neural network supervision control strategy for inverted pendulum tracking control. Discret Dyn Nat Soc 2021:1–14. https://doi.org/10.1155/2021/5536573

    Article  MathSciNet  Google Scholar 

  424. Chan RPM, Stol KA, Halkyard CR (2013) Review of modelling and control of two-wheeled robots. Annu Rev Control 37:89–103. https://doi.org/10.1016/j.arcontrol.2013.03.004

    Article  Google Scholar 

  425. Banerjee S (2005) Dynamics for engineers, 1st edn. Wiley, Kharagpur

    Google Scholar 

  426. Roubal J, Husek P, Stecha J (2010) Linearization: students forget the operating point. IEEE Trans Educ 53:413–418. https://doi.org/10.1109/TE.2009.2026427

    Article  Google Scholar 

  427. Tewari A (2002) Modern control design with MATLAB and SIMULINK, 1st edn. Wiley, Indian Institute of Technology

    Google Scholar 

  428. Rahmani A, Harib KH, Sureshkumar V, Oseni AO (2023) Stability control analysis of the double inverted pendulum using linear-quadratic regulator. In: 2023 advances in science and engineering technology international conferences (ASET). IEEE, Dubai, pp 1–5

  429. Maraslidis GS, Kottas TL, Tsipouras MG, Fragulis GF (2022) Design of a fuzzy logic controller for the double pendulum inverted on a cart. Information 13:379. https://doi.org/10.3390/info13080379

    Article  Google Scholar 

  430. Zhang S, Shao S, An R et al (2012) The sliding mode variable structure control for double inverted pendulum system based on fuzzy reaching law. In: Jin D, Lin S (eds) Advances in electronic engineering, communication and management, vol 1. Springer, Berlin, pp 123–129

    Chapter  Google Scholar 

  431. Banerjee R, Dey N, Mondal U, Hazra B (2018) Stabilization of double link inverted pendulum using LQR. In: 2018 international conference on current trends towards converging technologies (ICCTCT). IEEE, Coimbatore, pp 1–6

  432. Nejadfard A, Yazdanpanah MJ, Hassanzadeh I (2013) Friction compensation of double inverted pendulum on a cart using locally linear neuro-fuzzy model. Neural Comput Appl 22:337–347. https://doi.org/10.1007/s00521-011-0686-3

    Article  Google Scholar 

  433. Gohrle C, Schindler A, Wagner A, Sawodny O (2014) Design and vehicle implementation of preview active suspension controllers. IEEE Trans Contr Syst Technol 22:1135–1142. https://doi.org/10.1109/TCST.2013.2272342

    Article  Google Scholar 

  434. Hasbullah F, Faris WF, Darsivan FJ, Abdelrahman M (2019) Ride comfort performance of a non-linear full-car using active suspension system with active disturbance rejection control and input decoupling transformation. Int J Heavy Vehicle Syst 26:188–224

    Article  Google Scholar 

  435. Priyandoko G, Mailah M, Jamaluddin H (2009) Vehicle active suspension system using skyhook adaptive neuro active force control. Mech Syst Signal Process 23:855–868. https://doi.org/10.1016/j.ymssp.2008.07.014

    Article  Google Scholar 

  436. Liu B, Saif M, Fan H (2016) Adaptive fault tolerant control of a half-car active suspension systems subject to random actuator failures. IEEE/ASME Trans Mechatron 21:2847–2857. https://doi.org/10.1109/TMECH.2016.2587159

    Article  Google Scholar 

  437. Kazemipour A, Novinzadeh AB (2020) Adaptive fault-tolerant control for active suspension systems based on the terminal sliding mode approach. Proc Inst Mech Eng C J Mech Eng Sci 234:501–511. https://doi.org/10.1177/0954406219883304

    Article  Google Scholar 

  438. Nguyen ML, Tran TTH, Nguyen TA et al (2022) Application of MIMO control algorithm for active suspension system: a new model with 5 state variables. Lat Am J Solids Struct 19:e435. https://doi.org/10.1590/1679-78256992

    Article  Google Scholar 

  439. Gao H, Sun W, Shi P (2010) Robust sampled-data H-infinity control for vehicle active suspension systems. IEEE Trans Contr Syst Technol 18:238–245. https://doi.org/10.1109/TCST.2009.2015653

    Article  Google Scholar 

  440. Cao J, Li P, Liu H (2010) An interval fuzzy controller for vehicle active suspension systems. IEEE Trans Intell Transp Syst 11:885–895. https://doi.org/10.1109/TITS.2010.2053358

    Article  Google Scholar 

  441. Jia T, Pan Y, Liang H, Lam H-K (2022) Event-based adaptive fixed-time fuzzy control for active vehicle suspension systems with time-varying displacement constraint. IEEE Trans Fuzzy Syst 30:2813–2821. https://doi.org/10.1109/TFUZZ.2021.3075490

    Article  Google Scholar 

  442. Deshpande VS, Mohan B, Shendge PD, Phadke SB (2014) Disturbance observer based sliding mode control of active suspension systems. J Sound Vib 333:2281–2296. https://doi.org/10.1016/j.jsv.2014.01.023

    Article  Google Scholar 

  443. Chen S-A, Wang J-C, Yao M, Kim Y-B (2017) Improved optimal sliding mode control for a non-linear vehicle active suspension system. J Sound Vib 395:1–25. https://doi.org/10.1016/j.jsv.2017.02.017

    Article  Google Scholar 

  444. Alves UNLT, Garcia JPF, Teixeira MCM et al (2014) Sliding mode control for active suspension system with data acquisition delay. Math Probl Eng 2014:1–13. https://doi.org/10.1155/2014/529293

    Article  Google Scholar 

  445. Lin J, Lian R-J, Huang C-N, Sie W-T (2009) Enhanced fuzzy sliding mode controller for active suspension systems. Mechatronics 19:1178–1190. https://doi.org/10.1016/j.mechatronics.2009.03.009

    Article  Google Scholar 

  446. Al-Holou N, Lahdhiri T, Joo DS et al (2002) Sliding mode neural network inference fuzzy logic control for active suspension systems. IEEE Trans Fuzzy Syst 10:234–246. https://doi.org/10.1109/91.995124

    Article  Google Scholar 

  447. Shao X, Naghdy F, Du H (2017) Reliable fuzzy H-infinity control for active suspension of in-wheel motor driven electric vehicles with dynamic damping. Mech Syst Signal Process 87:365–383. https://doi.org/10.1016/j.ymssp.2016.10.032

    Article  Google Scholar 

  448. Chai L, Sun T (2010) The design of LQG controller for active suspension based on analytic hierarchy process. Math Probl Eng 2010:1–19. https://doi.org/10.1155/2010/701951

    Article  Google Scholar 

  449. Sun W, Gao H, Kaynak O (2013) Adaptive backstepping control for active suspension systems with hard constraints. IEEE/ASME Trans Mechatron 18:1072–1079. https://doi.org/10.1109/TMECH.2012.2204765

    Article  Google Scholar 

  450. Fialho I, Balas GJ (2002) Road adaptive active suspension design using linear parameter-varying gain-scheduling. IEEE Trans Contr Syst Technol 10:43–54. https://doi.org/10.1109/87.974337

    Article  Google Scholar 

  451. Singal K, Rajamani R (2013) Zero-energy active suspension system for automobiles with adaptive sky-hook damping. J Vib Acoust 135:011011. https://doi.org/10.1115/1.4007020

    Article  Google Scholar 

  452. Hu H, Wang Z (2002) Dynamics of controlled mechanical systems with delayed feedback. Springer, Berlin

    Book  Google Scholar 

  453. Pan H, Sun W, Gao H et al (2015) Nonlinear tracking control based on extended state observer for vehicle active suspensions with performance constraints. Mechatronics 30:363–370. https://doi.org/10.1016/j.mechatronics.2014.07.006

    Article  Google Scholar 

  454. Yonglin Z (2003) Time domain model of road irregularities simulated using the harmony superposition method. Trans Chin Soc Agric Eng 19:32–35

    Google Scholar 

  455. Kwon B, Kang D, Yi K (2020) Wheelbase preview control of an active suspension with a disturbance-decoupled observer to improve vehicle ride comfort. Proc Inst Mech Eng Part D 234:1725–1745. https://doi.org/10.1177/0954407019886499

    Article  Google Scholar 

  456. Zhang Z, Dong J (2023) A new optimization control policy for fuzzy vehicle suspension systems under membership functions online learning. IEEE Trans Syst Man Cybern Syst 53:3255–3266. https://doi.org/10.1109/TSMC.2022.3224739

    Article  Google Scholar 

  457. Jin X, Wang J, He X et al (2023) Improving vibration performance of electric vehicles based on in-wheel motor-active suspension system via robust finite frequency control. IEEE Trans Intell Transp Syst. https://doi.org/10.1109/TITS.2022.3224609

    Article  Google Scholar 

  458. Kim Y, Kwak T, Kanno M, Kim T-H (2023) Multi-objective finite-frequency H-infinity/GH-2 static output-feedback control synthesis for full-vehicle active suspension systems: a metaheuristic optimization approach. IEEE Access 11:36309–36330. https://doi.org/10.1109/ACCESS.2023.3266272

    Article  Google Scholar 

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  1. Electrical and Electronics Engineering Department, Nile University of Nigeria, Abuja, Nigeria

    Usman Mohammed, Tologon Karataev, Omotayo Oshiga & Oghorada Oghenewvogaga

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Mohammed, U., Karataev, T., Oshiga, O. et al. Comprehensive Review of Metaheuristic Algorithms (MAs) for Optimal Control (OCl) Improvement. Arch Computat Methods Eng (2024). https://doi.org/10.1007/s11831-023-10060-9

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