Model Reference Adaptive Control with Linear-like Closed-loop Behavior

TL;DR

This paper extends recent linear-like behavior results from pole-placement and $d$-step ahead control to the broader MRAC framework, ensuring exponential stability and bounded noise gain in adaptive control systems.

Contribution

It introduces a method to achieve linear-like closed-loop properties in MRAC using a convex set restriction on parameter estimates, enhancing robustness.

Findings

Achieves exponential stability in MRAC with linear-like behavior.

Provides bounded noise gain in the closed-loop system.

Demonstrates robustness to unmodelled dynamics and parameter variations.

Abstract

It is typically proven in adaptive control that asymptotic stabilization and tracking holds, and that at best a bounded-noise bounded-state property is proven. Recently, it has been shown in both the pole-placement control and the $d$-step ahead control settings that if, as part of the adaptive controller, a parameter estimator based on the original projection algorithm is used and the parameter estimates are restricted to a convex set, then the closed-loop system experiences linear-like behavior: exponential stability, a bounded gain on the noise in every $p$-norm, and a convolution bound on the exogenous inputs; this can be leveraged to provide tolerance to unmodelled dynamics and plant parameter time-variation. In this paper, we extend the approach to the more general Model Reference Adaptive Control (MRAC) problem and demonstrate that we achieve the same desirable linear-like closed-loop properties.