Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials

Abstract

This paper is dedicated to analyzing and presenting an efficient numerical algorithm for solving a class of fractional optimal control problems (FOCPs). The basic idea behind the suggested algorithm is based on transforming the FOCP under investigation into a coupled system of fractional-order differential equations whose solutions can be expanded in terms of the Jacobi basis. With the aid of the spectral-tau method, the problem can be reduced into a system of algebraic equations which can be solved via any suitable solver. Some illustrative examples and comparisons are presented aiming to demonstrate the accuracy, applicability, and efficiency of the proposed algorithm.

Keywords

• Jacobi polynomials
• tau method
• Newton's iterative method
• optimal control problems
• system of fractional differential equations