A class of nonlinear optimal control problems governed by Fredholm integro-differential equations with delay

ABSTRACT

This paper introduces an efficient numerical scheme for solving a significant class of nonlinear delay optimal control problem governed by Fredholm integro-differential equations. A direct approach based on a combination of block-pulse functions and orthonormal Taylor polynomials is utilised to transcribe the problem under study into a nonlinear programming one. The resulting optimisation problem is then solved by employing the method of Lagrange multipliers. An upper error bound for the hybrid functions with respect to the maximum norm is obtained. In addition, the convergence of the hybrid functions is established. Numerous numerical experiments are carried out to evaluate the performance and effectiveness of the suggested framework.

Keywords:

• Block-pulse functions
• orthonormal Taylor polynomials
• Fredholm integro-differential equation
• nonlinear optimal control
• time-delay system

Acknowledgments

The authors would like to express their sincere thanks to the reviewers for their useful comments and valuable suggestions that improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.