Model Reference Adaptive Control of Piecewise Affine Systems with State Tracking Performance Guarantees

TL;DR

This paper develops a model reference adaptive control method for uncertain piecewise affine systems, guaranteeing state tracking performance within a user-defined, time-varying bound, even with system switches and disturbances.

Contribution

It introduces a novel barrier Lyapunov function with a reset mechanism at switching instants, ensuring tracking error bounds without extra dwell time constraints.

Findings

Error metric remains within bounds during switching

Lyapunov function is non-increasing at switches

Method is validated through numerical example

Abstract

In this paper, we investigate the model reference adaptive control approach for uncertain piecewise affine systems with performance guarantees. The proposed approach ensures the error metric, defined as the weighted Euclidean norm of the state tracking error, to be confined within a user-defined time-varying performance bound. We introduce an auxiliary performance function to construct a barrier Lyapunov function. This auxiliary performance signal is reset at each switching instant, which prevents the transgression of the barriers caused by the jumps of the error metric at switching instants. The dwell time constraints are derived based on the parameters of the user-defined performance bound and the auxiliary performance function. We also prove that the Lyapunov function is non-increasing even at the switching instants and thus does not impose extra dwell time constraints. Furthermore, we propose the robust modification of the adaptive controller for the uncertain piecewise affine systems subject to unmatched disturbances. A Numerical example validates the correctness of the proposed approach.