Stabilization of Nonlinear Systems through Control Barrier Functions

TL;DR

This paper introduces a novel control design method that combines control barrier functions and Lyapunov functions to stabilize nonlinear systems, ensuring convergence even with discontinuities.

Contribution

It develops a new stabilization approach using nonsmooth control barrier functions and a weaker Lyapunov condition for nonlinear systems.

Findings

Controller guarantees asymptotic stability or convergence to a neighborhood

Method handles discontinuous control laws effectively

Demonstrated stability in various example systems

Abstract

This paper proposes a control design approach for stabilizing nonlinear control systems. Our key observation is that the set of points where the decrease condition of a control Lyapunov function (CLF) is feasible can be regarded as a safe set. By leveraging a nonsmooth version of control barrier functions (CBFs) and a weaker notion of CLF, we develop a control design that forces the system to converge to and remain in the region where the CLF decrease condition is feasible. We characterize the conditions under which our controller asymptotically stabilizes the origin or a small neighborhood around it, even in the cases where it is discontinuous. We illustrate our design in various examples.