Numerical Solution of Fractional Optimal Control

Wen Li (), Song Wang () and Volker Rehbock ()
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Wen Li: Curtin University
Song Wang: Curtin University
Volker Rehbock: Curtin University

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 2, No 11, 556-573

Abstract: Abstract This paper presents a numerical algorithm for solving a class of nonlinear optimal control problems subject to a system of fractional differential equations. We first propose a robust second-order numerical integration scheme for the system. The objective is approximated by the trapezoidal rule. We then apply a gradient-based optimization method to the discretized problem. Formulas for calculating the gradients are derived. Computational results demonstrate that our method is able to generate accurate numerical approximations for problems with multiple states and controls. It is also robust with respect to the fractional orders of derivatives.

Keywords: Fractional nonlinear optimal control; Numerical solution of fractional ODEs; Gradient-based algorithm; Gradient formula; 49M15; 49J15; 65L06 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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DOI: 10.1007/s10957-018-1418-y

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