论文标题
基于优化的安全稳定反馈，并有保证的吸引力区域
Optimization-Based Safe Stabilizing Feedback with Guaranteed Region of Attraction
论文作者
论文摘要
本文提出了一种基于惩罚的反馈设计框架的优化，以安全地稳定控制仿射系统。我们的起点是控制Lyapunov功能（CLF）和控制屏障功能（CBF）的可用性分别定义了输入中的仿射不等式，这些不等式分别证明了动态的稳定性和安全目标。提出的设计框架从惩罚方法中利用惩罚方法的思想将不平等之一作为硬约束，而另一种不平等作为软约束。我们研究了由此产生的反馈控制器下闭环系统的性质，并确定惩罚参数的条件，以消除可能出现的不良平衡。超出了文献中可用的局部稳定性保证，我们能够提供平衡吸引区域的内部近似，并确定整个安全集属于它的条件。模拟说明了我们的结果。
This paper proposes an optimization with penalty-based feedback design framework for safe stabilization of control affine systems. Our starting point is the availability of a control Lyapunov function (CLF) and a control barrier function (CBF) defining affine-in-the-input inequalities that certify, respectively, the stability and safety objectives for the dynamics. Leveraging ideas from penalty methods for constrained optimization, the proposed design framework imposes one of the inequalities as a hard constraint and the other one as a soft constraint. We study the properties of the closed-loop system under the resulting feedback controller and identify conditions on the penalty parameter to eliminate undesired equilibria that might arise. Going beyond the local stability guarantees available in the literature, we are able to provide an inner approximation of the region of attraction of the equilibrium, and identify conditions under which the whole safe set belongs to it. Simulations illustrate our results.
