Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method

A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a co...

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Bibliographic Details
Published in:Entropy (Basel, Switzerland) Vol. 22; no. 11; p. 1213
Main Authors: Chen, Shu-Bo, Soradi-Zeid, Samaneh, Jahanshahi, Hadi, Alcaraz, Raúl, Gómez-Aguilar, José Francisco, Bekiros, Stelios, Chu, Yu-Ming
Format: Journal Article
Language:English
Published: Switzerland MDPI 26.10.2020
MDPI AG
Subjects:
collocation points
delay system
direct optimization
fractional optimal control problem
nonlinear programming problem
radial basis function
radial basis function
fractional optimal control problem
direct optimization
nonlinear programming problem
collocation points
delay system
ISSN:1099-4300, 1099-4300
Online Access:Get full text
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Summary:A novel approach to solve optimal control problems dealing simultaneously with fractional differential equations and time delay is proposed in this work. More precisely, a set of global radial basis functions are firstly used to approximate the states and control variables in the problem. Then, a collocation method is applied to convert the time-delay fractional optimal control problem to a nonlinear programming one. By solving the resulting challenge, the unknown coefficients of the original one will be finally obtained. In this way, the proposed strategy introduces a very tunable framework for direct trajectory optimization, according to the discretization procedure and the range of arbitrary nodes. The algorithm’s performance has been analyzed for several non-trivial examples, and the obtained results have shown that this scheme is more accurate, robust, and efficient than most previous methods.
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ISSN:1099-4300
1099-4300
DOI:10.3390/e22111213