Title: On the relationship between control barrier functions and projected dynamical systems Show Chinese title

Title: 控制屏障函数与投影动力系统之间的关系

Abstract: In this paper, we study the relationship between systems controlled via Control Barrier Function (CBF) approaches and a class of discontinuous dynamical systems, called Projected Dynamical Systems (PDSs). In particular, under appropriate assumptions, we show that the vector field of CBF-controlled systems is a Krasovskii-like perturbation of the set-valued map of a differential inclusion, that abstracts PDSs. This result provides a novel perspective to analyze and design CBF-based controllers. Specifically, we show how, in certain cases, it can be employed for designing CBF-based controllers that, while imposing safety, preserve asymptotic stability and do not introduce undesired equilibria or limit cycles. Finally, we briefly discuss about how it enables continuous implementations of certain projection-based controllers, that are gaining increasing popularity. Show Chinese abstract

Abstract: 在本文中，我们研究通过控制屏障函数（CBF）方法控制的系统与一类称为投影动力系统（PDSs）的不连续动力系统之间的关系。特别地，在适当的假设下，我们证明了CBF控制系统的向量场是微分包含集值映射的类似Krasovskii的扰动，该微分包含抽象地表示PDSs。这一结果为分析和设计基于CBF的控制器提供了新的视角。具体来说，我们展示了在某些情况下，它可以用于设计基于CBF的控制器，这些控制器在施加安全性的同时保持渐近稳定性，并且不会引入不需要的平衡点或极限环。最后，我们简要讨论了它如何实现某些基于投影的控制器的连续实现，这些控制器正变得越来越受欢迎。