Cauchy discretization method for solve fractional linear optimal control problems

Abstract

This paper presents a numerical scheme designed for solving fractional linear optimal control problems (FLOCPs) governed by Caputo fractional derivatives (CFDs) of order 0<α≤1. The method transforms the original fractional control problem into an equivalent linear programming problem (LPP), enabling a more straightforward solution process. To evaluate the performance and accuracy of this approach, several numerical experiments were conducted using MATLAB. These experiments highlight the method’s computational efficiency and its simplicity in terms of implementation. The proposed approach offers accurate results, particularly in scenarios where traditional methods may fall short due to the complexities introduced by fractional derivatives. A detailed numerical example is presented to further illustrate the method’s effectiveness in addressing FLOCPs. The outcomes suggest that this approach is not only practical but also provides valuable insights for researchers dealing with fractional calculus in optimal control theory. This contribution is expected to be beneficial for applications in engineering and the physical sciences, where fractional-order systems play a significant role.