Adaptive Control of a First-Order System Providing Linear-Like Behaviour and Asymptotic Tracking
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Date
2021-07-19
Authors
Qazi, Hassaan Ali
Advisor
Miller, Daniel E.
Nielsen, Christopher
Nielsen, Christopher
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
Adaptive control is an approach used to deal with systems having uncertain and/or time-varying parameters. In 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 behaviour: exponential stability and a convolution bound on the input-output behaviour, 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 behaviour. 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 behaviour. 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.
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Keywords
adaptive control, exponential stability, linear-like behaviour, convolution bound