Taylor’s series expansion method for nonlinear variable-order fractional 2D optimal control problems

Abstract

This article introduces a category of variable-order fractional optimization problems subject to a partial differential equation. The Taylor’s series expansion method is developed as a suitable high-precision method for solving such problems. The proposed approach through the consecutive formulation describes how an optimization problem can be transformed into a system of algebraic equations using the Taylor’s series expansion. This achievement is significantly advantageous since the obtained algebraic system straightforwardly can be solved. The accuracy of the presented method is analyzed by solving a number of numerical examples.

Keywords

• Variable-order (VO)
• Taylor’s series expansion method
• Optimal control problems (OCPs)