A new approach to adaptive control: no nonlinearities

In adaptive control the goal is to design a controller to control an uncertain system whose parameters may be changing with time. Typically the controller consists of an identi-er (or tuner) which is used to adjust the parameters of a linear time-invariant (LTI) compensator, and under suitable assumptions on the plant model uncertainty it is proven that good asymptotic behaviour is achieved, such as model matching (for minimum phase systems) or stability. However, a typical adaptive controller does not track time-varying parameters very well, and it is often highly nonlinear, which can result in undesirable behaviour, such as large transients or a large control signal. Furthermore, most adaptive controllers provide only asymptotic tracking, with no ability to design for a pre-speci-ed settling time. 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. In this paper we argue the utility of this approach and then examine the -rst order case in detail, including a simulation. We also explore the bene-ts and limitations of the approach. c © 2003 Elsevier Science B.V. All rights reserved.