A linear time-varying approach to model reference adaptive control

Abstract

In classical model reference adaptive control, the goal is to design a controller to make the closed loop system act like a prespecified reference model in the face of significant plant uncertainty. Typically the controller consists of an identifier (or tuner) which is used to adjust the parameters of an LTI compensator, and under suitable assumptions on the plant model uncertainty it is proven that asymptotic matching is achieved. However, the controller is highly nonlinear, and the closed loop system can exhibit undesirable behaviour, such as large transients or a large control signal, especially if the initial parameter estimates are poor.

Here we propose an alternative approach, which yields a linear periodic controller. Rather than estimating the plant or compensator parameters, instead we estimate what the control signal would be if the plant parameters were known; we are able to do so in a linear fashion. In this paper we consider the first order case, and prove that if the plant parameters lie in a compact set, then near exact model matching can be achieved. We explore the benefits and limitations of the approach and explain how it can be extended to the relative degree one case.