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 theohpmtoa nonlinear ocp, the nonlinear two-point boundary value problem (tpbvp), derived from the pontryagin'smaximum principle, is transformed into a sequence of linear time-invariant tpbvp's. solving the latterproblems in a recursive manner provides the optimal trajectory and the optimal control law, in the form ofrapid convergent series. furthermore, the convergence of obtained series is controlled through a numberof auxiliary functions involving a number of constants, which are optimally determined. in this study, anefficient 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. theresults not only demonstrate the efficiency, simplicity and high accuracy of the suggested approach, butalso indicate its effectiveness in practical use.