Muntz-Legendre spectral collocation method for solving delay fractional optimal control problems

作     者：Hosseinpour, Soleiman Nazemi, Alireza Tohidi, Emran 

作者机构：Shahrood Univ Technol Fac Math Sci POB ***-316 Shahrood Iran Kosar Univ Bojnord Dept Math POB *** Bojnord Iran 

出 版 物：《JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS》 (计算与应用数学杂志)

年 卷 期：2019年第351卷

页      面：344-363页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：The authors are pleased to thank the anonymous referees and the editor for careful reading of our paper and for thoughtful and helpful suggestions 

主　　题：Delay fractional optimal control problem Operational matrix Muntz polynomials Pseudospectral method Pade approximation Nonlinear programming 

摘      要：In this paper, a numerical method is applied for solving delay fractional optimal control problems (DFOCPs). The fractional derivative is described in the Caputo sense. Since the fractional derivative of Muntz polynomials can be expressed in terms of the same polynomials, those polynomials can accurately represent properties of fractional calculus. In some situations such as in the frequency response based analysis of control systems containing a time-delay, it is necessary to substitute exponential function with an approximation in the form of a rational function. The most common approximation is the Pade approximation. At the first step, using Pade approximation, the delay problem is transformed to a non delay problem. Next, using the operational matrix of the fractional derivative of Mintz polynomials and pseudospectral method, fractional optimal control problem (FOCP) is reduced to a nonlinear programming problem. Some numerical examples are given to illustrate the effectiveness of the proposed scheme. (C) 2018 Elsevier B.V. All rights reserved.