Journal of Optimization Theory and Applications

, Volume 180, Issue 2, pp 556–573 | Cite as

Numerical Solution of Fractional Optimal Control

  • Wen Li
  • Song WangEmail author
  • Volker Rehbock


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.


Fractional nonlinear optimal control Numerical solution of fractional ODEs Gradient-based algorithm Gradient formula 

Mathematics Subject Classification

49M15 49J15 65L06 



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


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsCurtin UniversityPerthAustralia

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