Optimal control of nonlinear fractional order delay systems governed by Fredholm integral equations based on a new fractional derivative operator

Abstract

We aim to develop a direct transcription approach for solving a notable category of optimal control problems governed by nonlinear fractional Fredholm integral equations having delays in both input and output signals. The foundation of the new methodology is based on a multi domains decomposition scheme by utilizing the fractional-order Legendre functions. A new fractional derivative operator associated with the fractional basis is introduced by using the Caputo fractional derivative operator. With the use of derivative and delay operators, one can transform the dynamical system related to the fractional control problem into a new system containing algebraic equations. A wide variety of challenging test problems are studied to provide a detailed explanation of the designed approach.