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Moth-Flame Optimization Algorithm: Theory, Literature Review, and Application in Optimal Nonlinear Feedback Control Design

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Nature-Inspired Optimizers

Part of the book series: Studies in Computational Intelligence ((SCI,volume 811))

Abstract

A direct numerical method for optimal feedback control design of general nonlinear systems is presented in this chapter. The problem is generally infinite dimensional. In order to convert it to a finite dimensional optimization problem, a collocation type method is proposed. The collocation approach is based on approximating the control input function as a series of given base functions with unknown coefficients. Then, the optimal control problem is converted to the problem of finding a finite set of coefficients. To solve the resulting optimization problem, a new nature-inspired optimization paradigm known as Moth Flame Optimizer (MFO) is used. Validation and evaluating of accuracy of the method are performed via implementing it on some well known benchmark problems. Investigations presented in this chapter reveals the efficiency of the method and its benefits with respect to other numerical approaches. The chapter also consideres an in-depth literratur review and analysis of MFO.

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References

  1. Unal, C., & Salamci, M. U. (2018). Drug administration in cancer treatment via optimal nonlinear state feedback gain matrix design. IFAC Papersonline, 50, 9979–9984.

    Article  Google Scholar 

  2. Zhang, B., Liu, K., & Xiang, J. (2013). A stabilized optimal nonlinear feedback control for satellite attitude tracking. Aerospace Science and Technology, 27, 17–24.

    Article  Google Scholar 

  3. Mylvaganam, T., & Sassano, M. (2017). Approximate optimal control via measurement feedback for a class of nonlinear systems. IFAC Papersonline, 50, 15391–15396.

    Article  Google Scholar 

  4. Zhu, J. (2017). A feedback optimal control by Hamilton-Jacobi-Bellman equation. European Journal of Control, 37, 70–74.

    Article  MathSciNet  MATH  Google Scholar 

  5. Zheng, Y., & Cui, H. (2015). Optimal nonlinear feedback guidance algorithm for Mars powered descent. Aerospace Science and Technology, 45, 359–366.

    Article  MathSciNet  Google Scholar 

  6. Majumdar, A., Vasudevan, R., Tobenkin, M. M., & Tedrake, R. (2014). Convex Optimization of nonlinear feedback controllers via occupation measures. The International Journal of Robotics Research, 33, 1209–1230.

    Article  Google Scholar 

  7. Yun-jie, W., Futao, Z., & Chuang, S. (2017). Optimal discretization of feedback control in missile formation. Aerospace Science and Technology, 67, 456–472.

    Article  Google Scholar 

  8. Armaoua, A., & Ataei, A. (2014). Piece-wise constant predictive feedback control of nonlinear systems. Journal of Process Control, 24, 326–335.

    Article  Google Scholar 

  9. Xiao-Jun, T., Jian-Li, W., & Kai, C. (2015). A Chebyshev-Gauss pseudospectral method for solving optimal control problems. Acta Automatica Sinica, 41, 1778–1787.

    Article  MATH  Google Scholar 

  10. Mehne, S. H. H., & Mirjalili, S. (2018). A parallel numerical method for solving optimal control problems based on whale optimization algorithm. Knowl-Based System, 151, 114–123.

    Article  Google Scholar 

  11. Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in Engineering Software, 95, 51–67.

    Article  Google Scholar 

  12. Mirjalili, S. (2016). Dragonfly algorithm: A new meta-heuristic optimization technique for solving single-objective, discrete, and multi-objective problems. Neural Computing and Applications, 27, 1053–1073.

    Article  Google Scholar 

  13. Mirjalili, S., Gandomi, A. H., Mirjalili, S. Z., Saremi, S., Faris, H., & Mirjalili, S. M. (2017). Salp Swarm Algorithm: A bio-inspired optimizer for engineering design problems. Advances in Engineering Software, 114, 163–191.

    Article  Google Scholar 

  14. Kaveh, A., & Mahdavi, V. R. (2014). Colliding bodies optimization: A novel meta-heuristic method. Computers Structures, 139, 18–27.

    Article  Google Scholar 

  15. Kaveh, A., & Dadras, A. (2017). A novel meta-heuristic optimization algorithm: Thermal exchange optimization. Advances in Engineering Software, 110, 69–84.

    Article  Google Scholar 

  16. Mohamed, A. A., Mohamed, Y. S., El-Gaafary, A. A. M., & Hemeida, A. M. (2017). Optimal power flow using moth swarm algorithm. Electric Power Systems Research, 142, 190–206.

    Article  Google Scholar 

  17. Allam, D., Yousri, D. A., & Eteiba, M. B. (2016). Parameters extraction of the three diode model for the multi-crystalline solar cell/module using Moth-flame optimization algorithm. Energ Convers, 123, 535–54.

    Article  Google Scholar 

  18. Yamany, W., Fawzy, M., Tharwat, A., & Hassanien, A. E. (2016). Moth-flame optimization for training Multi-Layer Perceptrons. In 2015 11th International Computer Engineering Conference. https://doi.org/10.1109/ICENCO.2015.7416360.

  19. Abd El Azizab, M., Ewees, A. A., & Hassanien, A. E. (2017). Whale optimization algorithm and Moth-flame optimization for multilevel thresholding image segmentation. Expert Systems with Applications, 83, 242–256.

    Article  Google Scholar 

  20. Zhao, H., Zhao, H., & Guo, S. (2016). Using GM (1,1) Optimized by MFO with rolling mechanism to forecast the electricity consumption of inner mongolia. Applied Sciences, 6. https://doi.org/10.3390/app6010020.

  21. Yildiz, B. S., & Yildiz, A. R. (2017). Moth-flame optimization algorithm to determine optimal machining parameters in manufacturing processes. Materials Testing, 59, 425–429.

    Article  Google Scholar 

  22. Chitsaz, H., & Aminisharifabad, M. (2015). Exact learning of rna energy parameters from structure. Journal of Computational Biology, 22(6), 463–473.

    Article  MathSciNet  Google Scholar 

  23. Aminisharifabad, M., Yang, Q. & Wu, X. (2018). A penalized Autologistic regression with application for modeling the microstructure of dual-phase high strength steel. Journal of Quality Technology. in-press.

    Google Scholar 

  24. Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl-Based System, 89, 228–249.

    Article  Google Scholar 

  25. Reddy, S., Panwar, L. K., Panigrahi, B. K., & Kumar, R. (2018). Solution to unit commitment in power system operation planning using binary coded modified moth flame optimization algorithm (BMMFOA): A flame selection based computational technique. Journal of Computational Science, 25, 298–317. Multi-objective MFO.

    Google Scholar 

  26. Savsani, V., & Tawhid, M. A. (2017). Non-dominated sorting moth flame optimization (NS-MFO) for multi-objective problems. Engineering Applications of Artificial Intelligence, 63, 20–32.

    Article  Google Scholar 

  27. Nanda, S. J. (2016, September). Multi-objective moth flame optimization. In 2016 International Conference on Advances in Computing, Communications and Informatics (ICACCI) (pp. 2470–2476). IEEE.

    Google Scholar 

  28. Jangir, N., Pandya, M. H., Trivedi, I. N., Bhesdadiya, R. H., Jangir, P., & Kumar, A. (2016, March). Moth-Flame Optimization algorithm for solving real challenging constrained engineering optimization problems. In Electrical, Electronics and Computer Science (SCEECS), 2016 IEEE Students’ Conference on (pp. 1–5). IEEE.

    Google Scholar 

  29. Bhesdadiya, R. H., Trivedi, I. N., Jangir, P., & Jangir, N. (2018). Moth-flame optimizer method for solving constrained engineering optimization problems. In Advances in Computer and Computational Sciences (pp. 61–68). Springer, Singapore.

    Google Scholar 

  30. Apinantanakon, W., & Sunat, K. (2017, July). OMFO: A new opposition-based moth-flame optimization algorithm for solving unconstrained optimization problems. In International Conference on Computing and Information Technology pp. 22–31). Springer, Cham.

    Google Scholar 

  31. Emary, E., & Zawbaa, H. M. (2016). Impact of chaos functions on modern swarm optimizers. PloS One, 11(7), e0158738.

    Article  Google Scholar 

  32. Wang, M., Chen, H., Yang, B., Zhao, X., Hu, L., & Cai, Z., et al. (2017). Toward an optimal kernel extreme learning machine using a chaotic moth-flame optimization strategy with applications in medical diagnoses. Neurocomputing, 267, 69–84.

    Google Scholar 

  33. Guvenc, U., Duman, S., & Hnsloglu, Y. (2017, July). Chaotic moth swarm algorithm. In 2017 IEEE International Conference on INnovations in Intelligent SysTems and Applications (INISTA) (pp. 90–95). IEEE.

    Google Scholar 

  34. Li, Z., Zhou, Y., Zhang, S., & Song, J. (2016). Lvy-flight moth-flame algorithm for function optimization and engineering design problems. Mathematical Problems in Engineering.

    Google Scholar 

  35. Trivedi, I. N., Bhesdadiya, R. H., Pandya, M. H., Jangir, N., Jangir, P., & Ladumor, D. Implementation of meta-heuristic levy flight moth-flame optimizer for solving real challenging constrained engineering optimization problems.

    Google Scholar 

  36. Sayed, G. I., & Hassanien, A. E. (2018). A hybrid SA-MFO algorithm for function optimization and engineering design problems. Complex & Intelligent Systems, 1–18.

    Google Scholar 

  37. Bhesdadiya, R. H., Trivedi, I. N., Jangir, P., Kumar, A., Jangir, N., & Totlani, R. (2017). A novel hybrid approach particle swarm optimizer with moth-flame optimizer algorithm. In Advances in Computer and Computational Sciences (pp. 569-577). Springer, Singapore.

    Google Scholar 

  38. Anfal, M., & Abdelhafid, H. (2017). Optimal placement of PMUs in algerian network using a hybrid particle SwarmMoth flame optimizer (PSO-MFO). Electrotehnica, Electronica, Automatica, 65(3).

    Google Scholar 

  39. Jangir, P. (2017). Optimal power flow using a hybrid particle Swarm optimizer with moth flame optimizer. Global Journal of Research In Engineering.

    Google Scholar 

  40. Sarma, A., Bhutani, A., & Goel, L. (2017, September). Hybridization of moth flame optimization and gravitational search algorithm and its application to detection of food quality. In Intelligent Systems Conference (IntelliSys), 2017 (pp. 52–60). IEEE.

    Google Scholar 

  41. Zhang, L., Mistry, K., Neoh, S. C., & Lim, C. P. (2016). Intelligent facial emotion recognition using moth-firefly optimization. Knowledge-Based Systems, 111, 248–267.

    Article  Google Scholar 

  42. Li, C., Li, S., & Liu, Y. (2016). A least squares support vector machine model optimized by moth-flame optimization algorithm for annual power load forecasting. Applied Intelligence, 45(4), 1166–1178.

    Article  Google Scholar 

  43. Yamany, W., Fawzy, M., Tharwat, A., & Hassanien, A. E. (2015, December). Moth-flame optimization for training multi-layer perceptrons. In Computer Engineering Conference (ICENCO), 2015 11th International (pp. 267–272). IEEE.

    Google Scholar 

  44. Faris, H., Aljarah, I., & Mirjalili, S. (2017). Evolving radial basis function networks using MothFlame optimizer. In Handbook of Neural Computation (pp. 537–550).

    Google Scholar 

  45. Dosdoru, A. T., Boru, A., Gken, M., zalc, M., & Gken, T. (2018). Assessment of hybrid artificial neural networks and Metaheuristics for stock market forecasting. ukurova niversitesi Sosyal Bilimler Enstits Dergisi, 27(1), 63–78.

    Google Scholar 

  46. Kaur, N., Rattan, M., & Gill, S. S. (2018). Performance optimization of Broadwell-Y shaped transistor using artificial neural network and Moth-flame optimization technique. Majlesi Journal of Electrical Engineering, 12(1), 61–69.

    Google Scholar 

  47. Sayed, G. I., Soliman, M., & Hassanien, A. E. (2016). Bio-inspired swarm techniques for thermogram breast cancer detection. In Medical Imaging in Clinical Applications (pp. 487–506). Springer, Cham.

    Google Scholar 

  48. Sayed, G. I., & Hassanien, A. E. (2017). Moth-flame swarm optimization with neutrosophic sets for automatic mitosis detection in breast cancer histology images. Applied Intelligence, 47(2), 397–408.

    Article  Google Scholar 

  49. Diab, A. A. Z., & Rezk, H. Optimal sizing and placement of capacitors in radial distribution systems based on Grey Wolf, Dragonfly and MothFlame optimization algorithms. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 1–20.

    Google Scholar 

  50. Mohanty, B. (2018). Performance analysis of moth flame optimization algorithm for AGC system. International Journal of Modelling and Simulation, 1–15.

    Google Scholar 

  51. Mohanty, B., Acharyulu, B. V. S., & Hota, P. K. (2018). Mothflame optimization algorithm optimized dualmode controller for multiarea hybrid sources AGC system. Optimal Control Applications and Methods, 39(2), 720–734.

    Article  MathSciNet  MATH  Google Scholar 

  52. Barisal, A. K., & Lal, D. K. (2018). Application of moth flame optimization algorithm for AGC of multi-area interconnected power systems. International Journal of Energy Optimization and Engineering (IJEOE), 7(1), 22–49.

    Article  Google Scholar 

  53. Lal, D. K., Bhoi, K. K., & Barisal, A. K. (2016, October). Performance evaluation of MFO algorithm for AGC of a multi area power system. In 2016 International Conference on Signal Processing, Communication, Power and Embedded System (SCOPES) (pp. 903–908). IEEE.

    Google Scholar 

  54. Reddy, M. P. K., & Babu, M. R. (2017). A hybrid cluster head selection model for internet of things. Cluster Computing, 1–13.

    Google Scholar 

  55. Yang, X., Luo, Q., Zhang, J., Wu, X., & Zhou, Y. (2017, August). Moth Swarm algorithm for clustering analysis. In International Conference on Intelligent Computing (pp. 503–514). Springer, Cham.

    Google Scholar 

  56. Metwally, A. S., Hosam, E., Hassan, M. M., & Rashad, S. M. (2016, October). WAP: A novel automatic test generation technique based on moth flame optimization. In 2016 IEEE 27th International Symposium on Software Reliability Engineering (ISSRE) (pp. 59–64). IEEE.

    Google Scholar 

  57. Sharma, R., & Saha, A. (2017). Optimal test sequence generation in state based testing using moth flame optimization algorithm. Journal of Intelligent & Fuzzy Systems, (Preprint), 1–13.

    Google Scholar 

  58. Bhadoria, A., Kamboj, V. K., Sharma, M., & Bath, S. K. (2018). A solution to non-convex/convex and dynamic economic load dispatch problem using moth flame optimizer. INAE Letters, 3(2), 65–86.

    Article  Google Scholar 

  59. Trivedi, I. N., Kumar, A., Ranpariya, A. H., & Jangir, P. (2016, April). Economic load dispatch problem with ramp rate limits and prohibited operating zones solve using Levy Flight Moth-Flame optimizer. In 2016 International Conference on Energy Efficient Technologies for Sustainability (ICEETS) (pp. 442–447). IEEE.

    Google Scholar 

  60. Huang, Y., Ji, Z., Chen, Q., & Niu, S. (2017, September). Geographic atrophy segmentation for SD-OCT images by MFO algorithm and affinity diffusion. In International Conference on Intelligent Science and Big Data Engineering (pp. 473–484). Springer, Cham.

    Google Scholar 

  61. Mei, R. N. S., Sulaiman, M. H., Daniyal, H., & Mustaffa, Z. (2018). Application of Moth-flame optimizer and ant lion optimizer to solve optimal reactive power dispatch problems. Journal of Telecommunication, Electronic and Computer Engineering (JTEC), 10(1–2), 105–110.

    Google Scholar 

  62. Elsakaan, A. A., El-Sehiemy, R. A. A., Kaddah, S. S., & Elsaid, M. I. (2018). Economic power dispatch with emission constraint and valve point loading effect using moth flame optimization algorithm. In Advanced Engineering Forum (Vol. 28, pp. 139–149). Trans Tech Publications.

    Google Scholar 

  63. Trivedi, I. N., Parmar, S. A., Pandya, M. H., Jangir, P., Ladumor, D., & Bhoye, M. T. Optimal active and reactive power dispatch problem solution using Moth-Flame optimizer.

    Google Scholar 

  64. Anbarasan, P., & Jayabarathi, T. (2017). Optimal reactive power dispatch using Moth-flame optimization algorithm. International Journal of Applied Engineering Research, 12(13), 3690–3701.

    Google Scholar 

  65. Sulaiman, M. H., Mustaffa, Z., Aliman, O., Daniyal, H., & Mohamed, M. R. (2016). Application of moth-flame optimization algorithm for solving optimal reactive power dispatch problem.

    Google Scholar 

  66. Upper, N., Hemeida, A. M., & Ibrahim, A. A. (2017, December). Moth-flame algorithm and loss sensitivity factor for optimal allocation of shunt capacitor banks in radial distribution systems. In Power Systems Conference (MEPCON), 2017 Nineteenth International Middle East (pp. 851–856). IEEE.

    Google Scholar 

  67. Dhyani, A., Panda, M. K., & Jha, B. (2018). Moth-flame optimization-based fuzzy-PID controller for optimal control of active magnetic bearing system. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 1–13.

    Google Scholar 

  68. Saurav, S., Gupta, V. K., & Mishra, S. K. (2017, March). Moth-flame optimization based algorithm for FACTS devices allocation in a power system. In 2017 International Conference on Innovations in Information, Embedded and Communication Systems (ICIIECS) (pp. 1–7). IEEE.

    Google Scholar 

  69. Tolba, M. A., Diab, A. A. Z., Tulsky, V. N., & Abdelaziz, A. Y. (2018). LVCI approach for optimal allocation of distributed generations and capacitor banks in distribution grids based on mothflame optimization algorithm. Electrical Engineering, 1–26.

    Google Scholar 

  70. Gope, S., Dawn, S., Goswami, A. K., & Tiwari, P. K. (2016, November). Profit maximization with integration of wind farm in contingency constraint deregulated power market using Moth flame optimization algorithm. In Region 10 Conference (TENCON), 2016 IEEE (pp. 1462–1466). IEEE.

    Google Scholar 

  71. Ebrahim, M. A., Becherif, M., & Abdelaziz, A. Y. (2018). Dynamic performance enhancement for wind energy conversion system using Moth-flame optimization based blade pitch controller. Sustainable Energy Technologies and Assessments, 27, 206–212.

    Article  Google Scholar 

  72. GhobaeiArani, M., Rahmanian, A. A., Souri, A., & Rahmani, A. M. A mothflame optimization algorithm for web service composition in cloud computing: Simulation and verification. Software: Practice and Experience.

    Google Scholar 

  73. Khairuzzaman, A. K. M., & Chaudhury, S. (2017). Moth-flame optimization algorithm based multilevel thresholding for image segmentation. International Journal of Applied Metaheuristic Computing (IJAMC), 8(4), 58–83.

    Article  Google Scholar 

  74. Said, S., Mostafa, A., Houssein, E. H., Hassanien, A. E., & Hefny, H. (2017, September). Moth-flame optimization based segmentation for MRI liver images. In International Conference on Advanced Intelligent Systems and Informatics (pp. 320–330). Springer, Cham.

    Google Scholar 

  75. Muangkote, N., Sunat, K., & Chiewchanwattana, S. (2016, July). Multilevel thresholding for satellite image segmentation with moth-flame based optimization. In 2016 13th International Joint Conference on Computer Science and Software Engineering (JCSSE) (pp. 1–6). IEEE.

    Google Scholar 

  76. El Aziz, M. A., Ewees, A. A., & Hassanien, A. E. (2017). Whale optimization algorithm and Moth-flame optimization for multilevel thresholding image segmentation. Expert Systems with Applications, 83, 242–256.

    Article  Google Scholar 

  77. Li, W. K., Wang, W. L., & Li, L. (2018). Optimization of water resources utilization by multi-objective moth-flame algorithm. Water Resources Management, 1–14.

    Google Scholar 

  78. Das, A., Mandal, D., Ghoshal, S. P., & Kar, R. (2018). Concentric circular antenna array synthesis for side lobe suppression using moth flame optimization. AEU-International Journal of Electronics and Communications, 86, 177–184.

    Article  Google Scholar 

  79. Huang, L. N., Yang, B., Zhang, X. S., Yin, L. F., Yu, T., & Fang, Z. H. (2017). Optimal power tracking of doubly fed induction generator-based wind turbine using swarm mothflame optimizer. Transactions of the Institute of Measurement and Control, 0142331217712091.

    Google Scholar 

  80. Pathak, V. K., & Singh, A. K. (2017). Accuracy control of contactless laser sensor system using whale optimization algorithm and moth-flame optimization. tm-Technisches Messen, 84(11), 734–746.

    Google Scholar 

  81. Das, A., & Srivastava, L. Optimal placement and sizing of distributed generation units for power loss reduction using Moth-flame optimization algorithm.

    Google Scholar 

  82. Zou, L., Ge, B., & Chen, L. (2018). Range image registration based on hash map and moth-flame optimization. Journal of Electronic Imaging, 27(2), 023015.

    Article  Google Scholar 

  83. Sahu, P. C., Prusty, R. C., & Panda, S. (2017, April). MFO algorithm based fuzzy-PID controller in automatic generation control of multi-area system. In 2017 International Conference on Circuit, Power and Computing Technologies (ICCPCT) (pp. 1–6). IEEE.

    Google Scholar 

  84. Sayed, G. I., Hassanien, A. E., Nassef, T. M., & Pan, J. S. (2016, November). Alzheimers disease diagnosis based on Moth flame optimization. In International Conference on Genetic and Evolutionary Computing (pp. 298–305). Springer, Cham.

    Google Scholar 

  85. Gope, S., Dawn, S., Goswami, A. K., & Tiwari, P. K. (2016, November). Moth Flame optimization based optimal bidding strategy under transmission congestion in deregulated power market. In Region 10 Conference (TENCON), 2016 IEEE (pp. 617–621). IEEE.

    Google Scholar 

  86. Chauhan, S. S., & Kotecha, P. (2016, November). Single level production planning in petrochemical industries using Moth-flame optimization. In Region 10 Conference (TENCON), 2016 IEEE (pp. 263–266). IEEE.

    Google Scholar 

  87. Soliman, G. M., Khorshid, M. M., & Abou-El-Enien, T. H. (2016). Modified moth-flame optimization algorithms for terrorism prediction. International Journal of Application or Innovation in Engineering and Management, 5, 47–58.

    Google Scholar 

  88. Singh, P., & Prakash, S. (2017). Optical network unit placement in Fiber-Wireless (FiWi) access network by Moth-Flame optimization algorithm. Optical Fiber Technology, 36, 403–411.

    Article  Google Scholar 

  89. Mekhamer, S. F., Abdelaziz, A. Y., Badr, M. A. L., & Algabalawy, M. A. (2015). Optimal multi-criteria design of hybrid power generation systems: A new contribution. International Journal of Computer Applications, 129(2), 13–24.

    Article  Google Scholar 

  90. Ewees, A. A., Sahlol, A. T., & Amasha, M. A. (2017, May). A Bio-inspired moth-flame optimization algorithm for Arabic handwritten letter recognition. In 2017 International Conference on Control, Artificial Intelligence, Robotics & Optimization (ICCAIRO) (pp. 154–159). IEEE.

    Google Scholar 

  91. Zhao, H., Zhao, H., & Guo, S. (2016). Using GM (1, 1) optimized by MFO with rolling mechanism to forecast the electricity consumption of inner mongolia. Applied Sciences, 6(1), 20.

    Article  Google Scholar 

  92. Zawbaa, H. M., Emary, E., Parv, B., & Sharawi, M. (2016, July). Feature selection approach based on moth-flame optimization algorithm. In 2016 IEEE Congress on Evolutionary Computation (CEC) (pp. 4612–4617). IEEE.

    Google Scholar 

  93. Patil, D., Mulla, A., Chakraborty, D., & Pillai, H. (2015). Computation of feedback control for time optimal state transfer using Groebner basis. Systems & Control Letters, 79, 1–7.

    Article  MathSciNet  MATH  Google Scholar 

  94. Jabbari Asl, H., & Yoon, J. (2016). Power capture optimization of variable-speed wind turbines using an output feedback controller. Renewable Energy, 86, 517–525.

    Article  Google Scholar 

  95. Zhou, H., Chen, C., Lai, J., Lu, X., Deng, Q., Gao, X., et al. (2018). Affine nonlinear control for an ultra-supercritical coal fired once-through boiler-turbine unit. Energy, 153, 638–649.

    Article  Google Scholar 

  96. Tavakoli, M., Taghirad, H. D., & Abrishamchian, M. (2005). Identification and robust H control of the rotational/translational actuator system. International Journal of Control, Automation, 3, 387–396.

    Google Scholar 

  97. Gao, B., & Ye, F. (2014). Dynamical analysis and stabilizing control of inclined rotational translational actuator systems. Journal of Applied Mathematics,. https://doi.org/10.1155/2014/598384.

    Article  MATH  Google Scholar 

  98. Kumar, A., & Sharma, R. (2017). Fuzzy lyapunov reinforcement learning for non linear systems. ISA Transactions, 67, 151–159.

    Article  Google Scholar 

  99. Bupp, R. T., Bernstein, D. S., & Coppola, V. T. (1998). A benchmark problem for nonlinear control design. International Journal Robust Nonlinear Control, 8, 307–310.

    Article  MathSciNet  Google Scholar 

  100. Luo, B, Wu, H. N., Huang, T, & Derong Liu, D. Data-based approximate policy iteration for affine nonlinear continuous-time optimal control design. Automatica, 50, 3281–3290.

    Google Scholar 

  101. Cimen, T., & Banks, S. P. (2004). Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria. Systems Control Letters, 53, 327–346.

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

Authors would like to thank Mr. Farhad Karimzadeh for performing some of the graphical tasks.

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Authors and Affiliations

  1. Aerospace Research Institute, 1465774111, Tehran, Iran

    Seyed Hamed Hashemi Mehne

  2. School of Information and Communication Technology, Griffith University, Nathan Campus, Brisbane, QLD, 4111, Australia

    Seyedali Mirjalili

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Correspondence to Seyedali Mirjalili .

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  1. Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, QLD, Australia

    Seyedali Mirjalili

  2. Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, QLD, Australia

    Jin Song Dong

  3. Institute for Integrated and Intelligent Systems, Griffith University, Brisbane, QLD, Australia

    Andrew Lewis

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Mehne, S.H.H., Mirjalili, S. (2020). Moth-Flame Optimization Algorithm: Theory, Literature Review, and Application in Optimal Nonlinear Feedback Control Design. In: Mirjalili, S., Song Dong, J., Lewis, A. (eds) Nature-Inspired Optimizers. Studies in Computational Intelligence, vol 811. Springer, Cham. https://doi.org/10.1007/978-3-030-12127-3_9

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