Discrete Minimum Time Control via Iterative Optimization and Sliding Window Algorithm

In this paper we propose a new objective function for the discrete minimum time control problem, where constraints in control are allowed. With this objective function, the control problem is transformed into a tractable optimization problem where traditional numerical algorithms can be applied. We proved that under some conditions, the optimal solution of the newly transformed problem yields the minimum time of the original problem. We propose a Sliding Window Algorithm which dynamically adjusts a time window aiming to catch the optimal solution, and for problems with constraints we propose a constrained interior search algorithm. Numerical examples are provided to show the effectiveness of our algorithms.