TY - JOUR JF - IJMSI JO - IJMSI VL - 15 IS - 2 PY - 2020 Y1 - 2020/10/01 TI - The Numerical Solution of Some Optimal Control Systems with Constant and Pantograph Delays via Bernstein Polynomials TT - N2 - ‎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. SP - 163 EP - 181 AU - Ghaderi, N. AU - Farahi, M. H. AD - Ferdowsi university of mashhad KW - Optimal control with pantograph systems‎ KW - ‎Optimal control with time delay‎ KW - ‎Pantograph delay differential equation‎ KW - ‎Bernstein polynomials. UR - http://ijmsi.ir/article-1-1154-en.html ER -