Dynamic programming method for constrained discrete-time optimal control

A dynamic programming method is presented for solving constrained, discrete-time, optimal control problems. The method is based on an efficient algorithm for solving the subproblems of sequential quadratic programming. By using an interior-point method to accommodate inequality constraints, a modification of an existing algorithm for equality constrained problems can be used iteratively to solve the subproblems. Two test problems and two application problems are presented. The application examples include a rest-to-rest manoeuvre of a flexible structure and a constrained brachistochrone problem.