Optimal control of time delay Fredholm integro-differential equations

This paper is devoted to solve a set of non-linear optimal control problems which are touched with time-delay  Fredholm integro-differential equations. The serious objective of this work  is to contribute  an appropriate   direct scheme for solving these problems. The technique used  in this paper  is based upon the Dickson polynomials and collocation points. Getting through the solutions, the states and controls variables can be approximated with  Dickson polynomials. Therefore, the  optimal control problem with  time-delay   integro-differential equation   transforms  into a system of algebraic equations that by solving it, we can obtain the unknown coefficients of the main problem. The residual  error estimation of this technique is also investigated. Accuracy amount of the absolute errors have been studied for the performance of this method by solving several non-trivial examples.