A Novel Successive Approximation Method for Solving a Class of Optimal Control Problems

Document Type: Research articles


1 Department of mathematics, Faculty of basic sciences, University of Neyshabur, Neyshabur, IRAN.

2 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.