论文标题
混合动力学系统集合的正向不变性（第二部分）
Forward Invariance of Sets for Hybrid Dynamical Systems (Part II)
论文作者
论文摘要
本文介绍了用于设计控制定律的工具，该工具诱导了用于混合动力学的混合动力系统集合的强大控制的正向不变性。如果闭环系统的每个解决方案始于集合，则一组可以通过控制定律具有强大的控制向前不变性属性，而不管干扰的价值如何，该集合从集合中停留在集合中。在本文（Chai and Sanfelice，2019年）的本文第一部分的基础上，在本文中，提出了足够的通用套装条件，可以享受此类财产。为了构建诱导状态反馈定律的不变性，定义了鲁棒控制Lyapunov功能的概念。提出的合成结果依赖于设定值的图，其中包括所有可允许的控制输入，这些输入将封闭环解决方案保留在感兴趣的集合中。还提出了保证存在此类国家反馈法律的结果。此外，还提供了设计具有最低点标准的连续状态反馈定律的条件。在本文中，在约束的弹跳系统和机器人操作器应用中说明了主要结果。
This article presents tools for the design of control laws inducing robust controlled forward invariance of a set for hybrid dynamical systems modeled as hybrid inclusions. A set has the robust controlled forward invariance property via a control law if every solution to the closed-loop system that starts from the set stays within the set for all future time, regardless of the value of the disturbances. Building on the first part of this article, which focuses on analysis (Chai and Sanfelice, 2019), in this article, sufficient conditions for generic sets to enjoy such a property are proposed. To construct invariance inducing state-feedback laws, the notion of robust control Lyapunov function for forward invariance is defined. The proposed synthesis results rely on set-valued maps that include all admissible control inputs that keep closed-loop solutions within the set of interest. Results guaranteeing the existence of such state-feedback laws are also presented. Moreover, conditions for the design of continuous state-feedback laws with minimum point-wise norm are provided. Major results are illustrated throughout this article in a constrained bouncing ball system and a robotic manipulator application.
