‎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.

Keywords: Optimal control with pantograph systems‎, ‎Optimal control with time delay‎, ‎Pantograph delay differential equation‎, ‎Bernstein polynomials.

Full-Text [PDF 200 kb]