Formulation of Euler-Lagrange Equations for Multidelay Fractional Optimal Control Problems

被引：16

作者：

Effati, Sohrab ^{[1
]}

Rakhshan, Seyed Ali ^{[1
]}

Saqi, Samane ^{[1
]}

机构：

[1] Ferdowsi Univ Mashhad, Dept Appl Math, Mashhad 917751159, Iran

来源：

JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS | 2018年 / 13卷 / 06期

关键词：

fractional calculus; time-delay; Euler-Lagrange; Grunwald-Letnikov derivative; DELAY SYSTEMS; DIFFERENTIAL-EQUATIONS; LEGENDRE POLYNOMIALS; NUMERICAL-SOLUTION; MAXIMUM PRINCIPLE; LINEAR-SYSTEMS; BLOCK-PULSE; TIME-DELAY; CALCULUS; HYBRID;

D O I：

10.1115/1.4039900

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

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.

引用

页数：10

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