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

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.