Optimal Control Computation for Discrete Time Time-delayed Optimal Control Problem with All-time-step Inequality Constraints

In this paper, we consider a class of discrete time optimal control problems with time delay and subject to nonlinear all-time-step inequality constraints on both the state and control. By using a constraint transcription technique in conjunction with a local smoothing method, the problem is approximated by a sequence of discrete time optimal control problems with time delay and subject to nonlinear inequality constraints in canonical form. Rigorous analysis is carried out, showing the convergence of the optimal solutions of the approximate problems to the optimal solution of the original problem. We then move on to consider a general class of discrete time optimal control problems with time delay and subject to nonlinear constraints in canonical form. A computational method is developed based on the sequential quadratic programming (SQP) approximation scheme with active set strategy. It solves the discrete time optimal control problem with time delay and subject to canonical constraints as a nonlinear optimization problem. As an application, we consider a tactical logistic decision analysis problem, which is formulated as a discrete time optimal control problems with time delay and subject to alltime-step inequality constraints. Using the computational method proposed, this practical problem is solved effectively, producing much better results than those obtained in existing literature.