Numerical Solution of Fractional Optimal Control

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...

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Bibliographic Details
Main Authors: Li, W., Wang, Song, Rehbock, Volker
Format: Journal Article
Published: Springer New York LLC 2018
Online Access:http://hdl.handle.net/20.500.11937/72834
Description
Summary: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.