A highly computational efficient method to solve nonlinear optimal control problems

In this paper, a new analytical technique, called the Optimal Homotopy Perturbation Method (OHPM), is suggested to solve a class of nonlinear Optimal Control Problems (OCP's). Applying the OHPM to a nonlinear OCP, the nonlinear Two-Point Boundary Value Problem (TPBVP), derived from the Pontryagin's maximum principle, is transformed into a sequence of linear time-invariant TPBVP's. Solving the latter problems in a recursive manner provides the optimal trajectory and the optimal control law, in the form of rapid convergent series. Furthermore, the convergence of obtained series is controlled through a number of auxiliary functions involving a number of constants, which are optimally determined. In this study, an efficient algorithm is also presented, which has low computational complexity and fast convergence rate. Just a few iterations are required to find a suboptimal trajectory-control pair for the nonlinear OCP. The results not only demonstrate the efficiency, simplicity and high accuracy of the suggested approach, but also indicate its effectiveness in practical use. (C) 2012 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.