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.
Highlights
Fractional calculus is a very important branch of mathematical analysis
A fractional optimal control problems (FOCPs) is an optimal control problem in which the criterion and/or the differential equations governing the dynamics of the system contain at least one fractional derivative operator
The spectral-tau Jacobi algorithm (STJA) is employed for handling some FOCPs accompanied with some comparisons hoping to demonstrate the efficiency and applicability of the
Summary
Fractional calculus is a very important branch of mathematical analysis. This branch of calculus is interested in generalizing the derivatives and integrals of integer order to include derivatives and integrals of an arbitrary order (real or complex). Spectral tau algorithm for solving a class of fractional optimal control problems via Jacobi polynomials 153 physics, chemistry and fluid mechanics. The Galerkin approach requires to select suitable basis functions satisfying the boundary conditions and enforcing the residual to be orthogonal with the basis functions This method has been applied in a variety of papers. This paper introduces a general numerical algorithm for a class of FOCPs. A FOCP is an optimal control problem in which the criterion and/or the differential equations governing the dynamics of the system contain at least one fractional derivative operator. Analyzing efficient spectral-tau algorithm for handling the resulting system of fractional-order differential equations via Jacobi polynomials.
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