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Optimal Control of Time-Delay Fractional Equations via a Joint Application of Radial Basis Functions and Collocation Method
Authors:Shu-Bo Chen,Samaneh Soradi-Zeid,Hadi Jahanshahi,Raú  l Alcaraz,José   Francisco Gó  mez-Aguilar,Stelios Bekiros,Yu-Ming Chu
Abstract: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.
Keywords:fractional optimal control problem   delay system   radial basis function   direct optimization   collocation points   nonlinear programming problem
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