A Numerical Approach for Solving Nonlinear Optimal Control Problems Using the Hybrid Scheme of Fitness Dependent Optimizer and Bernstein Polynomials

Abstract

In this paper, a heuristic scheme based on the hybridization of Bernstein Polynomials (BPs) and nature-inspired optimization techniques is presented to achieve the numerical solution of Nonlinear Optimal Control Problems (NOCPs) efficiently. The solution of NOCP is approximated by the linear combination of BPs with unknown coefficients. The unknown coefficients are estimated by transforming the NOCP into an error minimization problem and formulating the objective function. The Genetic Algorithm (GA) and Fitness Dependent Optimizer (FDO) are used for solving the objective function and obtaining the optimum values of the unknown coefficients. The findings and statistical results indicate the represented hybrid scheme offers encouraging results and outperforms the most recent and popular methods proposed in the literature, which ultimately validates the efficacy and productivity of the recommended approach. Furthermore, statistical analysis is incorporated to examine the reliability and stability of the suggested technique. Consequently, the remarkable difference is evident in simplicity, flexibility, and effectiveness compared to the other methods considered.

Keywords

• Optimal control problems
• optimization problem
• Bernstein polynomials
• fitness dependent optimizer
• genetic algorithm