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

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.(c) 2022 ISA. Published by Elsevier Ltd. All rights reserved.

Automated summary

This research aims to develop a direct transcription approach for solving optimal control problems governed by nonlinear fractional Fredholm integral equations with delays in input and output signals. The new methodology is based on a multi domains decomposition scheme using fractional-order Legendre functions. A new fractional derivative operator associated with the fractional basis is introduced using the Caputo fractional derivative operator. The dynamical system related to the fractional control problem is transformed into a new system of algebraic equations using derivative and delay operators. Various challenging test problems are studied to demonstrate the effectiveness of the designed approach.