Numerical Solution of Fractional Optimal Control

• Published in: Journal of optimization theory and applications Vol. 180; no. 2; pp. 556 - 573
• Main Authors: Li, Wen, Wang, Song, Rehbock, Volker
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2019; Springer Nature B.V
• Subjects: Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Differential equations; Engineering; Mathematics; Mathematics and Statistics; Nonlinear control; Numerical analysis; Numerical integration; Operations Research/Decision Theory; Optimal control; Optimization; Production planning; Robustness (mathematics); Theory of Computation; Gradient-based algorithm; 65L06; Fractional nonlinear optimal control; Gradient formula; Numerical solution of fractional ODEs; 49M15; 49J15
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-018-1418-y

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.