On Compatibility and Region of Attraction for Safe, Stabilizing Control Laws

Abstract

A novel control method is proposed to ensure compatibility of safe, stabilizing control laws, i.e., simultaneous satisfaction of asymptotic stability and constraint satisfaction for nonlinear affine systems. The results are dependent on an asymptotically stabilizing control law and a zeroing control barrier function (ZCBF), but do not require a control Lyapunov function (CLF). Sufficient conditions for a region of attraction are defined for which the proposed control safely stabilizes the system, while preserving the decrescent Lyapunov function of the original stabilizing control law. The proposed methodology for nonlinear affine systems requires checking conditions of the system dynamics over a substantial portion of the state space, which may be computationally expensive. To facilitate the search for compatibility, we extend the results to a class of nonlinear systems including mechanical systems for which a novel controller is designed to guarantee passivity, safety, and stability. Numerical examples are used to demonstrate the proposed technique.

To appear: IEEE Transactions on Automatic Control

References in corpus (3)

• Control Barrier Function based Quadratic Programs Introduce Undesirable Asymptotically Stable Equilibria
• Provably Safe Control of Lagrangian Systems in Obstacle-Scattered Environments
• High-order Barrier Functions: Robustness, Safety and Performance-Critical Control

Cited by in corpus (5)

• Continuous Approximations of Projected Dynamical Systems via Control Barrier Functions
• Control Synthesis for Stability and Safety by Differential Complementarity Problem
• On the relationship between control barrier functions and projected dynamical systems
• On the Undesired Equilibria Induced by Control Barrier Function Based Quadratic Programs
• Independence of Closed-Loop Equilibria and Stability from the Choice of Control Barrier Function for a Given Safe Set