A novel gradient-based discrete time-delayed optimization algorithm for optimal control problems with Caputo–Fabrizio fractional derivative

Abstract

In this paper, we consider a class of fractional optimal control problems (FOCPs) involving the Caputo–Fabrizio (CF) derivative operator. The Adams–Bashforth numerical integration method is used to discretize the fractional-order system, and the trapezoidal rule is introduced to approximate the cost function. Interestingly, this leads to a discrete-time time-delay optimal control problem. On this basis, we derive the gradient formulae of the cost and constraint functions with respect to decision variables and we propose a novel normalization function for the CF derivative operator. Then, a gradient-based optimization algorithm is designed to solve this discrete-time time-delay optimal control problem. Finally, numerical simulations of three example problems are performed to illustrate the effectiveness of the developed algorithm.