Safe Stabilization using Nonsmooth Control Lyapunov Barrier Function

TL;DR

This paper introduces a nonsmooth Control Lyapunov Barrier Function (NCLBF) framework that guarantees safe stabilization of systems, overcoming limitations of smooth functions and validated through theoretical analysis and simulations.

Contribution

We propose a novel NCLBF approach that ensures safe stabilization and controller feasibility, extending control design to multiple unsafe regions.

Findings

NCLBF guarantees safe stabilization in linear and nonlinear systems.

The approach outperforms existing smooth Lyapunov barrier methods.

Simulations validate the effectiveness of the proposed method.

Abstract

This paper addresses the challenge of safe stabilization, ensuring the system state reach the origin while avoiding unsafe regions. Existing approaches relying on smooth Lyapunov barrier functions often fail to guarantee a feasible controller. To overcome this limitation, we introduce the nonsmooth Control Lyapunov Barrier Function (NCLBF), which ensures the existence of a safe and stabilizing controller. We provide a systematic framework for designing NCLBF and feedback control strategies to achieve safe stabilization in the presence of multiple bounded unsafe regions. Theoretical analysis and simulations of both linear and nonlinear systems demonstrate the effectiveness and superiority of our approach compared to the existing smooth functions method.