Title: Nonlinear and linear approaches to adaptive control (1 hour)
Abstract: In classical model reference adaptive control, the goal is to design a controller to make the closed loop system act like a prespecifed 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, expecially if the initial parameter estimates are poor.
After providing an overview of the classical approach, we discuss 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. We explore the benefits and limitations of the approach and compare it to the classical one.