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

  • Seyed Hamed Hashemi Mehne
  • Seyedali MirjaliliEmail author
Part of the Studies in Computational Intelligence book series (SCI, volume 811)


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.



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


  1. 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.CrossRefGoogle Scholar
  2. 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.CrossRefGoogle Scholar
  3. 3.
    Mylvaganam, T., & Sassano, M. (2017). Approximate optimal control via measurement feedback for a class of nonlinear systems. IFAC Papersonline, 50, 15391–15396.CrossRefGoogle Scholar
  4. 4.
    Zhu, J. (2017). A feedback optimal control by Hamilton-Jacobi-Bellman equation. European Journal of Control, 37, 70–74.MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zheng, Y., & Cui, H. (2015). Optimal nonlinear feedback guidance algorithm for Mars powered descent. Aerospace Science and Technology, 45, 359–366.MathSciNetCrossRefGoogle Scholar
  6. 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.CrossRefGoogle Scholar
  7. 7.
    Yun-jie, W., Futao, Z., & Chuang, S. (2017). Optimal discretization of feedback control in missile formation. Aerospace Science and Technology, 67, 456–472.CrossRefGoogle Scholar
  8. 8.
    Armaoua, A., & Ataei, A. (2014). Piece-wise constant predictive feedback control of nonlinear systems. Journal of Process Control, 24, 326–335.CrossRefGoogle Scholar
  9. 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.CrossRefGoogle Scholar
  10. 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.CrossRefGoogle Scholar
  11. 11.
    Mirjalili, S., & Lewis, A. (2016). The whale optimization algorithm. Advances in Engineering Software, 95, 51–67.CrossRefGoogle Scholar
  12. 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.CrossRefGoogle Scholar
  13. 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.CrossRefGoogle Scholar
  14. 14.
    Kaveh, A., & Mahdavi, V. R. (2014). Colliding bodies optimization: A novel meta-heuristic method. Computers Structures, 139, 18–27.CrossRefGoogle Scholar
  15. 15.
    Kaveh, A., & Dadras, A. (2017). A novel meta-heuristic optimization algorithm: Thermal exchange optimization. Advances in Engineering Software, 110, 69–84.CrossRefGoogle Scholar
  16. 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.CrossRefGoogle Scholar
  17. 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.CrossRefGoogle Scholar
  18. 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.
  19. 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.CrossRefGoogle Scholar
  20. 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. Scholar
  21. 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.CrossRefGoogle Scholar
  22. 22.
    Chitsaz, H., & Aminisharifabad, M. (2015). Exact learning of rna energy parameters from structure. Journal of Computational Biology, 22(6), 463–473.MathSciNetCrossRefGoogle Scholar
  23. 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. 24.
    Mirjalili, S. (2015). Moth-flame optimization algorithm: A novel nature-inspired heuristic paradigm. Knowl-Based System, 89, 228–249.CrossRefGoogle Scholar
  25. 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.MathSciNetCrossRefGoogle Scholar
  26. 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.CrossRefGoogle Scholar
  27. 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. 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. 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. 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. 31.
    Emary, E., & Zawbaa, H. M. (2016). Impact of chaos functions on modern swarm optimizers. PloS One, 11(7), e0158738.CrossRefGoogle Scholar
  32. 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.CrossRefGoogle Scholar
  33. 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. 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. 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. 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. 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.CrossRefGoogle Scholar
  38. 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. 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. 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. 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.CrossRefGoogle Scholar
  42. 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.CrossRefGoogle Scholar
  43. 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. 44.
    Faris, H., Aljarah, I., & Mirjalili, S. (2017). Evolving radial basis function networks using MothFlame optimizer. In Handbook of Neural Computation (pp. 537–550).CrossRefGoogle Scholar
  45. 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. 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. 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.CrossRefGoogle Scholar
  48. 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.CrossRefGoogle Scholar
  49. 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. 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. 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.MathSciNetCrossRefGoogle Scholar
  52. 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.CrossRefGoogle Scholar
  53. 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. 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. 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.CrossRefGoogle Scholar
  56. 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. 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. 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.CrossRefGoogle Scholar
  59. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.CrossRefGoogle Scholar
  72. 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. 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.CrossRefGoogle Scholar
  74. 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. 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. 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.CrossRefGoogle Scholar
  77. 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. 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.CrossRefGoogle Scholar
  79. 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. 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. 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. 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.CrossRefGoogle Scholar
  83. 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. 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. 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. 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. 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. 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.CrossRefGoogle Scholar
  89. 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.CrossRefGoogle Scholar
  90. 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. 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.CrossRefGoogle Scholar
  92. 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. 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.MathSciNetCrossRefGoogle Scholar
  94. 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.CrossRefGoogle Scholar
  95. 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.CrossRefGoogle Scholar
  96. 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. 97.
    Gao, B., & Ye, F. (2014). Dynamical analysis and stabilizing control of inclined rotational translational actuator systems. Journal of Applied Mathematics,. Scholar
  98. 98.
    Kumar, A., & Sharma, R. (2017). Fuzzy lyapunov reinforcement learning for non linear systems. ISA Transactions, 67, 151–159.CrossRefGoogle Scholar
  99. 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.MathSciNetCrossRefGoogle Scholar
  100. 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.MathSciNetCrossRefGoogle Scholar
  101. 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.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Seyed Hamed Hashemi Mehne
    • 1
  • Seyedali Mirjalili
    • 2
    Email author
  1. 1.Aerospace Research InstituteTehranIran
  2. 2.School of Information and Communication TechnologyGriffith UniversityBrisbaneAustralia

Personalised recommendations