An Effective Differential Dynamic Programming Algorithm for Constrained Optimal Control Problems

This paper presents a new differential dynamic programming (DDP) algorithm for solving constrained optimal control problems. The basic idea is to relax all constraints but the system dynamics by using the multiplier method. For a given set of multipliers, there is an unconstrained dynamic optimization problem to which DDP applies effectively. The optimal solution is obtained by iteratively updating multipliers and solving the corresponding dynamic optimization problem. This new algorithm is convergent, easy to implement, and applicable to problems with quite general constraints and system dynamics.