Multilevel Techniques for the Solution of HJB Minimum-Time Control Problems

Abstract

The solution of minimum-time feedback optimal control problems is generally achieved using the dynamic programming approach, in which the value function must be computed on numerical grids with a very large number of points. Classical numerical strategies, such as value iteration (VI) or policy iteration (PI) methods, become very inefficient if the number of grid points is large. This is a strong limitation to their use in real-world applications. To address this problem, the authors present a novel multilevel framework, where classical VI and PI are embedded in a full-approximation storage (FAS) scheme. In fact, the authors will show that VI and PI have excellent smoothing properties, a fact that makes them very suitable for use in multilevel frameworks. Moreover, a new smoother is developed by accelerating VI using Anderson’s extrapolation technique. The effectiveness of our new scheme is demonstrated by several numerical experiments.