论文标题
通过差分互补问题控制稳定性和安全性的控制综合
Control Synthesis for Stability and Safety by Differential Complementarity Problem
论文作者
论文摘要
本文开发了一种新型的控制合成方法，用于将控制疗法系统的安全稳定作为差异互补问题（DCP）。我们的设计使用控制Lyapunov功能（CLF）和控制屏障功能（CBF）来定义DCP公式中的互补性约束，以证明稳定性和安全性。 CLF-CBF-DCP控制器将稳定性作为软约束施加，当安全约束处于活动状态时，它会自动放松，而无需参数调整或优化。我们使用CLF-CBF-DCP控制器研究闭环系统行为，并确定有关局部均衡存在的条件。尽管在某些情况下，控制器会产生不良的局部平衡，但可以通过正确选择控制参数将其局限于安全集边界的一小部分。然后，我们的方法可以避免CLF-CBF二次编程技术遇到的不良平衡。
This paper develops a novel control synthesis method for safe stabilization of control-affine systems as a Differential Complementarity Problem (DCP). Our design uses a control Lyapunov function (CLF) and a control barrier function (CBF) to define complementarity constraints in the DCP formulation to certify stability and safety, respectively. The CLF-CBF-DCP controller imposes stability as a soft constraint, which is automatically relaxed when the safety constraint is active, without the need for parameter tuning or optimization. We study the closed-loop system behavior with the CLF-CBF-DCP controller and identify conditions on the existence of local equilibria. Although in certain cases the controller yields undesirable local equilibria, those can be confined to a small subset of the safe set boundary by proper choice of the control parameters. Then, our method can avoid undesirable equilibria that CLF-CBF quadratic programming techniques encounter.
