OPTIMAL CONTROL OF NONLINEAR TIME-DELAY FRACTIONAL DIFFERENTIAL EQUATIONS WITH DICKSON POLYNOMIALS

Shu-Bo Chen, Samaneh Soradi-Zeid, Maryam Alipour, Yu-Ming Chu, J. F. Gã“mez-Aguilar and Hadi Jahanshahi
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Shu-Bo Chen: School of Science, Hunan City University, Yiyang 413000, P. R. China
Samaneh Soradi-Zeid: ��Faculty of Industry and Mining (Khash), University of Sistan and Baluchestan, Zahedan, Iran
Maryam Alipour: ��Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran
Yu-Ming Chu: �Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China¶Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science & Technology, Changsha 410114, P. R. China
J. F. Gã“mez-Aguilar: ��CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México
Hadi Jahanshahi: *Department of Mechanical Engineering, University of Manitoba, Winnipeg R3T 5V6, Canada

FRACTALS (fractals), 2021, vol. 29, issue 04, 1-16

Abstract: In this paper, a novel direct scheme to solve a set of time-delay fractional optimal control problems is introduced. The method firstly uses a set of Dickson polynomials as basis functions to approximate the states and control variables of the system. Next, the context of these basis functions and the use of a collocation method allow to transform the problem into a system of nonlinear algebraic equations. Finally, the unknown coefficients and control parameters in the original problem can be easily estimated by resolving the new system of equations. Given the high efficiency of the Dickson polynomials to deal with time-delay fractional systems, the proposed strategy involves a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The convergence analysis of the proposed method is presented, along with some illustrative examples which demonstrate its most relevant features.

Keywords: Fractional Optimal Control Problem; Delay System; Dickson Polynomials; Direct Optimization; Collocation Points; Algebraic Equations (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500791

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