The Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials

In this paper, we present a numerical method based on Bernstein polynomials to solve optimal control systems with constant and pantograph delays. Constant or pantograph delays may appear in state-control or both. We derive delay operational matrix and pantograph operational matrix for Bernstein polynomials then, these are utilized to reduce the solution of optimal control with constant and pantograph delay to the solution of nonlinear programming. In truth, the principal problem can be transferred to the quadratic programming problem. Some examples are included to demonstrate the validity and applicability of the technique.