Safe and Stable Adaptive Control for a Class of Dynamic Systems

TL;DR

This paper introduces a novel adaptive control method that combines control barrier functions with real-time adaptation to ensure stability and safety in linear time-invariant systems with uncertainties and input constraints.

Contribution

It develops a new adaptive control framework integrating CBFs for safety and stability guarantees in uncertain linear systems with input limits.

Findings

Guarantees stability and safety despite parametric uncertainties.

Successfully applied to obstacle avoidance and missile control scenarios.

Provides conditions for stability, convergence, and parameter learning.

Abstract

Adaptive control has focused on online control of dynamic systems in the presence of parametric uncertainties, with solutions guaranteeing stability and control performance. Safety, a related property to stability, is becoming increasingly important as the footprint of autonomous systems grows in society. One of the popular ways for ensuring safety is through the notion of a control barrier function (CBF). In this paper, we combine adaptation and CBFs to develop a real-time controller that guarantees stability and remains safe in the presence of parametric uncertainties. The class of dynamic systems that we focus on is linear time-invariant systems whose states are accessible and where the inputs are subject to a magnitude limit. Conditions of stability, state convergence to a desired value, and parameter learning are all elucidated. One of the elements of the proposed adaptive controller that ensures stability and safety is the use of a CBF-based safety filter that suitably generates safe reference commands, employs error-based relaxation (EBR) of Nagumo's theorem, and leads to guarantees of set invariance. To demonstrate the effectiveness of our approach, we present two numerical examples, an obstacle avoidance case and a missile flight control case.