A Fixed-Time Stable Adaptation Law for Safety-Critical Control under Parametric Uncertainty

TL;DR

This paper introduces a fixed-time stable adaptation law combined with a robust control barrier function to ensure safe control of nonlinear systems with parametric uncertainty, guaranteeing rapid convergence and safety.

Contribution

A novel fixed-time stable adaptation law integrated with a robust adaptive control barrier function for safety-critical control under parametric uncertainty.

Findings

Guarantees convergence of parameter estimates within fixed time

Ensures safe control despite model uncertainties

Demonstrates effectiveness in an automobile overtaking scenario

Abstract

We present a novel technique for solving the problem of safe control for a general class of nonlinear, control-affine systems subject to parametric model uncertainty. Invoking Lyapunov analysis and the notion of fixed-time stability (FxTS), we introduce a parameter adaptation law which guarantees convergence of the estimates of unknown parameters in the system dynamics to their true values within a fixed-time independent of the initial parameter estimation error. We then synthesize the adaptation law with a robust, adaptive control barrier function (RaCBF) based quadratic program to compute safe control inputs despite the considered model uncertainty. To corroborate our results, we undertake a comparative case study on the efficacy of this result versus other recent approaches in the literature to safe control under uncertainty, and close by highlighting the value of our method in the context of an automobile overtake scenario.