Application of optimization algorithm to nonlinear fractional optimal control problems

Asma Moradikashkooli ¹ (Department of Computer Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran)
Hamid Haj Seyyed Javadi ² (Department of Computer Engineering, Shahed University, Tehran, Iran)
Sam Jabbehdari ³ (Department of Computer Engineering, North Tehran Branch, Islamic Azad University, Tehran, Iran)

Submited date : 2023-09-18 accepted date : 2023-10-27

Keywords: generalized Laguerre polynomials, Operational matrix, Optimization algorithm, Nonlinear fractional optimal control problems, Coefficients and parameters,

Abstract :

In this study, an optimization algorithm based on the generalized Laguerre polynomials (GLPs) as the basis functions and the Lagrange multipliers is presented to obtain approximate solution of nonlinear fractional optimal control problems. The Caputo fractional derivatives of GLPs is constructed. The operational matrices of the Caputo and ordinary derivatives are introduced. The established scheme transforms obtaining the solution of such problems into finding the solution of algebraic systems of equations by approximating the state and control variables using the mentioned basis functions. The method is very accurate and is computationally very attractive. Examples are included to provide the capacity of the proposal method.