Candidate: Hassaan Qazi
Title: Adaptive Control of a First-Order System Providing Linear-Like Behavior and Asymptotic Tracking
Date: June 29, 2021
Time: 11:00 AM
Supervisor(s): Nielsen, Christopher - Miller, Daniel
This thesis, we consider the problem of designing an adaptive controller for a discrete-time first-order plant. Recently, Shahab et.al. considered this problem and proposed an approach which provides linear-like behavior: exponential stability and aconvolution bound on the input-output behavior, together with robustness to slow time-variations and unmodelled dynamics. However, asymptotic tracking of a general reference signal was not provided.
Here, we extend the aforementioned work with the aim to achieve asymptotic tracking while retaining linear-like closed-loop behavior. We replace this uncertainty set with a pair of convex sets, one for each sign of the input gain, which enables us to use two parameter estimators -- one for each convex set. We design these estimators using the modified version of the original projection algorithm. For each estimator, there is the corresponding one-step-ahead control law. A dynamic performance signal based switching rule is then adopted that decides which controller should be used at each time step. It is shown that the proposed approach preserves linear-like behavior. In addition to that, we also have shown asymptotic trajectory tracking for two different circumstances: when the reference signal is asymptotically strongly persistently exciting of order two, and for a fairly general reference signal but the plant is unstable. Numerical simulations are presented to demonstrate the efficacy of the proposed approach.