Iterative calculation of optimal control trajectories for nonlinear systems

In this paper we introduce an algorithm that solves the nonlinear optimal control problem (NLOCP) iteratively by solving a series of linear time varying optimal control problems (LTVOCP). Starting from an initial pair of input/state trajectories, in each step of the algorithm an optimal perturbation of the trajectories that produces the fastest decrease of the cost functional is obtained and the trajectories are improved. Convergence of the algorithm to the optimal set of trajectories is ensured. The results are presented in the framework of Pontryagin's minimum principle (PMP). It is shown via different examples that the proposed algorithm is more efficient and robust compared to some other methods. The proposed algorithm finds the optimal solution in some of the cases in which the other methods fail.