UWSpace is currently experiencing technical difficulties resulting from its recent migration to a new version of its software. These technical issues are not affecting the submission and browse features of the site. UWaterloo community members may continue submitting items to UWSpace. We apologize for the inconvenience, and are actively working to resolve these technical issues.
 

Supervisory Adaptive Control Revisited: Linear-like Convolution Bounds

Thumbnail Image

Files

Lalumiere_Craig.pdf (1.93 MB)

Date

2022-08-23

Authors

Lalumiere, Craig

Journal Title

Journal ISSN

Volume Title

Publisher

University of Waterloo

Abstract

Classical feedback control for LTI systems enjoys many desirable properties including exponential stability, a bounded noise-gain, and tolerance to a degree of unmodeled dynamics. However, an accurate model for the system must be known. The field of adaptive control aims to allow one to control a system with a great deal of parametric uncertainty, but most such controllers do not exhibit those nice properties of an LTI system, and may not tolerate a time-varying plant. In this thesis, it is shown that an adaptive controller constructed via the machinery of Supervisory Control yields a closed-loop system which is exponentially stable, and where the effects of the exogenous inputs are bounded above by a linear convolution - this is a new result in the Supervisory Control literature. The consequences of this are that the system enjoys linear-like properties: it has a bounded noise-gain, is robust to a degree of unmodeled dynamics, and is tolerant of a degree of time-varying plant parameters. This is demonstrated in two cases: the first is the typical application of Supervisory Control - an integral control law is used to achieve step tracking in the presence of a constant disturbance. It is shown that the tracking error exponentially goes to zero when the disturbance is constant, and is bounded above by a linear convolution when it is not. The second case is a new application of Supervisory Control: it is shown that for a minimum phase plant, the d-step-ahead control law may be used to achieve asymptotic tracking of an arbitrary bounded reference signal. In addition to the convolution bound, a crisp bound is found on the 1-norm of the tracking error when a disturbance is absent.

Description

Keywords

adaptive control, supervisory control, exponential stability, bounded gain, adaptive tracking, control systems, convolution bound

LC Keywords

Citation

URI

http://hdl.handle.net/10012/18614

Collections

Theses
Electrical and Computer Engineering