An efficient numerical method for the optimal control of fractional-order dynamic systems

Abstract

This paper aims to investigate an efficient numerical scheme for the optimal control of fractional-order dynamic systems. By using the Grünwald–Letnikov approximation for the fractional derivatives and introducing a new transformation in the calculus of variations, the fractional optimal control problem under consideration is converted into a linear programming problem. Then, the internal model principle is employed in order to extend the new scheme for the fractional dynamic systems affected by the external persistent disturbances. Numerical examples and comparative results verify the validity and applicability of the new technique.