Adaptive Control Barrier Functions with Vanishing Conservativeness Under Persistency of Excitation

TL;DR

This paper introduces an adaptive control barrier function method that reduces conservativeness over time under persistency of excitation, enabling better constraint satisfaction in uncertain systems.

Contribution

It proposes a closed-form adaptive CBF approach with vanishing conservativeness using recursive least squares and persistency of excitation conditions.

Findings

Successfully ensures constraint satisfaction in nonlinear systems.

Demonstrates improved performance with vanishing conservativeness.

Validates approach through numerical examples with a pendulum and robot.

Abstract

This article presents a closed-form adaptive controlbarrier-function (CBF) approach for satisfying state constraints in systems with parametric uncertainty. This approach uses a sampled-data recursive-least-squares algorithm to estimate the unknown model parameters and construct a nonincreasing upper bound on the norm of the estimation error. Together, this estimate and upper bound are used to construct a CBF-based constraint that has nonincreasing conservativeness. Furthermore, if a persistency of excitation condition is satisfied, then the CBFbased constraint has vanishing conservativeness in the sense that the CBF-based constraint converges to the ideal constraint corresponding to the case where the uncertainty is known. In addition, the approach incorporates a monotonically improving estimate of the unknown model parameters thus, this estimate can be effectively incorporated into a desired control law. We demonstrate constraint satisfaction and performance using 2 two numerical examples, namely, a nonlinear pendulum and a nonholonomic robot.