Comparison of metaheuristic optimization algorithms for numerical solutions of optimal control problems

Abstract

Summary The objective in optimal control problems is to determine the control rule to be applied according to the objective function determined for a given system. Theoretically, different solution methods have been developed starting from calculus of variation such as Pontriagin, Hamilton, or Riccati. In this study, apart from analytical methods, it is proposed to apply algorithms inspired by nature to the same problem. Among these algorithms, genetic algorithm, firefly algorithm, Harris Hawk's optimization algorithm, and differential evolution optimization algorithm have been applied to given optimal control problems and their successes were compared in terms of statistical analysis such as minimum, maximum, average, Wilcoxon, and Friedman analysis. The originality of this study is to control the system with discrete control rule by partitioning the control signal, to be applied to the system which is wanted to be optimally controlled. This will allow the control of different techniques, such as MPC or NMPC, which will contribute to the determination of the global optimum control rule, especially in the solution of nonlinear systems. In addition, three different applications have been performed to demonstrate. As a result of these experiments, it has been shown that these algorithms can be applied successfully to such problems.