Abstract
Conference Title: 2018 IEEE Conference on Decision and Control (CDC) Conference Start Date: 2018, Dec. 17 Conference End Date: 2018, Dec. 19 Conference Location: FL, USA Classical adaptive controllers provide asymptotic stabilization; neither exponential stability nor a bounded noise gain is typically proven. In recent work it is shown that these desired properties can be achieved by using an estimator based on the original ideal Projection Algorithm (together with a restriction of the parameter estimates to a given compact convex set), rather than the commonly used modified classical algorithm. Here the goal is to remove the convexity requirement. To this end, we consider the first-order case with unknown plant parameters belonging to a compact uncertainty set of controllable pairs. The first step of our approach is to observe that the compact uncertainty set can be covered by a finite number of convex compact sets, each of controllable pairs. For each of the convex compact sets, we design an estimator together with the corresponding one-step-ahead controller, and apply a switching logic to choose between them. We prove that the resulting controller guarantees linear-like convolution bounds on the closed-loop behavior, which implies exponential stability and a bounded noise gain.