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

作     者：CIARAMELLA Gabriele FABRINI Giulia CIARAMELLA Gabriele;FABRINI Giulia

作者机构：Department of Mathematics and StatisticsUniversity of KonstanzKonstanz 78464Germany 

出 版 物：《Journal of Systems Science & Complexity》 (系统科学与复杂性学报（英文版）)

年 卷 期：2021年第34卷第6期

页      面：2069-2091页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

主　　题：Anderson acceleration FAS Hamilton-Jacobi equation minimum-time problem multi-level acceleration methods policy iteration value iteration 

摘      要：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 *** numerical strategies,such as value iteration(VI)or policy iteration(PI)methods,become very inefficient if the number of grid points is *** is a strong limitation to their use in real-world *** address this problem,the authors present a novel multilevel framework,where classical VI and PI are embedded in a full-approximation storage(FAS)*** fact,the authors will show that VI and PI have excellent smoothing properties,a fact that makes them very suitable for use in multilevel ***,a new smoother is developed by accelerating VI using Anderson’s extrapolation *** effectiveness of our new scheme is demonstrated by several numerical experiments.