Extended Hybrid Model Reference Adaptive Control of Piecewise Affine Systems

TL;DR

This paper extends hybrid adaptive control methods to handle disturbances in piecewise affine systems, ensuring stability and convergence even with affine terms and sliding solutions.

Contribution

It introduces an adaptive control extension that guarantees global convergence and bounded adaptive gains for piecewise affine systems with disturbances.

Findings

Proves global convergence using a common Lyapunov function.

Ensures boundedness of adaptive gains.

Handles disturbances due to affine terms in plant and reference model.

Abstract

This note presents an extension to the adaptive control strategy presented in [1] able to counter eventual instability due to disturbances at the input of an otherwise $\mathcal{L}_2$ stable closed-loop system. These disturbances are due to the presence of affine terms in the plant and reference model. The existence of a common Lyapunov function is used to prove global convergence of the error system, even in the presence of sliding solutions, as well as boundedness of all the adaptive gains.