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research-article

Numerical Schemes for Fractional Optimal Control Problems

[+] Author and Article Information
Ali Alizadeh

Department of Mathematics Payame Noor University P.O.Box 19395-3697 Tehran, Iran
alizadeh312@gmail.com

Sohrab Effati

Department of Applied Mathematics Ferdowsi University of Mashhad Mashhad, Iran
s-effati@um.ac.ir

Aghileh Heydari

Department of Mathematics Payame Noor University P.O.Box 19395-3697 Tehran, Iran
a_heidari@pnu.ac.ir

1Corresponding author.

ASME doi:10.1115/1.4035533 History: Received May 22, 2016; Revised December 10, 2016

Abstract

In the present study, variational iteration and Adomian decomposition methods are applied for solving a class of fractional optimal control problems (FOCPs). Also a comparative study between these two methods is presented. The fractional derivative in these problems is in the Caputo sense. To solve the problem, first the necessary optimality conditions of FOCP are achieved for a linear tracking fractional optimal control problem and then these two methods are used to solve the resulting fractional differential equations. It is shown that the modified Adomian decomposition method and variational iteration method use the same iterative formula for solving linear and nonlinear FOCPs. The convergence of the modified Adomian decomposition method is analytically studied and to illustrate the validity and applicability of the methods, some examples are provided.

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