محمد شیرازیان - Department of mathematics, Faculty of basic sciences, University of Neyshabur, Neyshabur, IRAN.
سهراب عفتی - Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran.

This paper presents a successive approximation method (SAM) for solving a large class of optimal control problems. The proposed analytical-approximate method, successively solves the Two-Point Boundary Value Problem (TPBVP), obtained from the Pontryagin's Maximum Principle (PMP). The convergence of this method is proved and a control design algorithm with low computational complexity is presented. Through the finite number of algorithm iterations, a suboptimal control law is obtained for the optimal control problem. An illustrative example is given to demonstrate the efficiency of the proposed method.

Optimal control problem, Successive approximation method, Pontryagin's maximum principle, Suboptimal control