In this paper, a new numerical scheme is proposed for multidelay fractional order optimal control problems where its derivative is considered in the Grunwald–Letnikov sense. We develop generalized Euler–Lagrange equations that results from multidelay fractional optimal control problems (FOCP) with final terminal. These equations are created by using the calculus of variations and the formula for fractional integration by parts. The derived equations are then reduced into system of algebraic equations by using a Grunwald–Letnikov approximation for the fractional derivatives. Finally, for confirming the accuracy of the proposed approach, some illustrative numerical examples are solved.
Formulation of Euler–Lagrange Equations for Multidelay Fractional Optimal Control Problems
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 27, 2017; final manuscript received April 4, 2018; published online May 2, 2018. Assoc. Editor: Zaihua Wang.
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Effati, S., Ali Rakhshan, S., and Saqi, S. (May 2, 2018). "Formulation of Euler–Lagrange Equations for Multidelay Fractional Optimal Control Problems." ASME. J. Comput. Nonlinear Dynam. June 2018; 13(6): 061007. https://doi.org/10.1115/1.4039900
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