A Method for Constrained Dynamic Optimization Problems

Optimal control problems are difficult to solve because of their inherent complexity. Among existing computational methods, one class of algorithms utilize the Differential Dynamic Programming (DDP) concept. DDP is quite efficient for unconstrained problems. However, because of the difficulties caused by the propagation of constraints through system dynamics, there has not been a systematic DDP type algorithm for constrained problems by using the primal approach. In this paper, a new DDP method for solving linearly constrained optimal control problems by using the primal approach is presented. By appropriately incorporating the facial descriptive method to delineate admissible regions, our algorithm has no special requirements on the part of state and control matrices. Numerical results show that the algorithm is suitable for general linear constrained optimal control problems, and the computation time increases almostly linearly as the time horizon increases.