A new approach to differential dynamic programming for discrete time systems

This paper proposes a new differential dynamic programming algorithm for solving discrete time optimal control problems with equality and inequality constraints on both control and state variables and proves its convergence. The present algorithm is different from differential dynamic programming algorithms developed in [10]-[15], which can hardly solve optimal control problems with inequality constraints on state variables and whose convergence has not been proved. Composed of iterative methods for solving systems of nonlinear equations, it is based upon Kuhn-Tucker conditions for recurrence relations of dynamic programming. Numerical examples show file efficiency of the present algorithm.