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research-article

Formulation of Euler-Lagrange equations for multi-delay fractional optimal control problems

[+] Author and Article Information
Sohrab Effati

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

Seyed Ali Rakhshan

Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
seyedalirakhshan@yahoo.com

Samane Saqi

Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
samane.saqi@mail.um.ac.ir

1Corresponding author.

ASME doi:10.1115/1.4039900 History: Received November 27, 2017; Revised April 04, 2018

Abstract

This article presents the approximation for solving the fractional optimal control problems with delays in state and control variables. The fractional derivative is considerd in the Grunwald-Letnikov sense. The Calculus of Variations, the Lagrange multiplier, and the formula for fractional integration by parts are used to obtain Euler-Lagrange equations for the multi-delay fractional optimal control problem. For numerical computation, the multi-delay fractional dynamic system are approximated using the Grunwald-Letnikov definition. This leads to a set of algebraic equations that can be solved using numerical techniques. We illustrate the effectiveness of the procedure with four examples.

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