Hamilton-Jacobi-Bellman Equation for Control Systems With Friction

• 成果类型: Article
• 署名作者: Tedone, Fabio; Palladino, Michele
• 署名单位: Gran Sasso Science Institute (GSSI)
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.3040726
• 发表日期: 2021
• 页码: 5651-5664
• 关键词: Differential inclusion; friction; invariance principles; optimal control; value function

摘要

This article proposes a new framework for modeling control systems, in which a dynamic friction occurs. The model consists of a controlled differential inclusion with a discontinuous right-hand side, which still preserves existence and uniqueness of the solution for each given input function u(t). Under general hypotheses, we are able to derive the Hamilton-Jacobi-Bellman equation for the related free-time-optimal control problem and to characterize the value function as the unique locally Lipschitz continuous viscosity solution.