Journal of Optimization Theory and Applications

, Volume 180, Issue 2, pp 556–573

# Numerical Solution of Fractional Optimal Control

• Wen Li
• Song Wang
• Volker Rehbock
Article

## 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

## Mathematics Subject Classification

49M15 49J15 65L06

## Notes

### Acknowledgements

This work is supported by US Air Force Office of Scientific Research Project FA2386-15-1-4095.

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© Springer Science+Business Media, LLC, part of Springer Nature 2018

## Authors and Affiliations

• Wen Li
• 1
• Song Wang
• 1
• Volker Rehbock
• 1
1. 1.Department of Mathematics and StatisticsCurtin UniversityPerthAustralia