A highly computational efficient method to solve nonlinear optimal control problems

Abstract

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.