Numerical Method for Solving Fractional Order Optimal Control Problems with Free and Non-Free Terminal Time

Abstract

The optimal control theory in mathematics aims to study the finding of control for a dynamic system over time, where an objective function is optimized. It has a broad range of applications in engineering, operations research, and science. The main purpose of this study is to provide numerical algorithms for two cases of optimal control problems of fractional order that involve fractional order derivatives with free and non-free terminal time. In addition to comparing the numerical results for three test problems with exact solutions of these problems, various computer simulations are also introduced.

Keywords

• optimal control
• fractional differential equations (FDEs)
• fractional optimal control problems (FOCPs)
• free terminal time