Adaptive Safety-Critical Control for a Class of Nonlinear Systems with Parametric Uncertainties: A Control Barrier Function Approach

TL;DR

This paper introduces an adaptive control method using control barrier functions for nonlinear systems with parametric uncertainties, ensuring safety and avoiding singularities through a closed-form solution and data-driven improvements.

Contribution

It proposes a novel adaptive safety-critical control framework combining control barrier functions with explicit solutions, independent of online parameter estimation.

Findings

Verifies non-emptiness of control set independently of parameter estimates

Provides a closed-form solution for safe control synthesis

Demonstrates effectiveness through numerical simulations

Abstract

This paper presents a novel approach for the safe control design of systems with parametric uncertainties in both drift terms and control-input matrices. The method combines control barrier functions and adaptive laws to generate a safe controller through a nonlinear program with an explicitly given closed-form solution. The proposed approach verifies the non-emptiness of the admissible control set independently of online parameter estimations, which can ensure the safe controller is singularity-free. A data-driven algorithm is also developed to improve the performance of the proposed controller by tightening the bounds of the unknown parameters. The effectiveness of the control scheme is demonstrated through numerical simulations.