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

TL;DR

This paper introduces a control method that ensures safe, stabilizing control laws for nonlinear affine systems, combining stability and safety constraints without needing a control Lyapunov function, and extends to mechanical systems.

Contribution

It proposes a new approach to achieve compatibility of safety and stability in control laws without relying on a control Lyapunov function, applicable to nonlinear and mechanical systems.

Findings

The method guarantees safe stabilization within a defined region of attraction.

It extends to mechanical systems, ensuring passivity, safety, and stability.

Numerical examples demonstrate the effectiveness of the proposed control approach.

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.