Time Optimal Control and Switching Curve Analysis for Caputo Fractional Systems

Abstract

In this paper we present a method for fractional time optimal control problems in terms of Caputo fractional derivatives. The studies up to now are about systems in terms of Riemann-Liouville fractional derivatives. But in this paper we investigated Caputo fractional systems. Firstly, by utilizing matrix approach method to discrete fractional derivatives, fractional Caputo derivative is solved. Then, the original problem is solved by traditional optimal problem solvers. Finally, time optimal problem is studied for a double fractional integrator and a method for obtaining switching curve has presented.