The University of Southampton
University of Southampton Institutional Repository

Adaptive control and robustness in the gap metric

Record type: Article

We consider the construction of adaptive controllers for minimum phase linear systems which achieve non-zero robustness margins in the sense of the gap metric. The gap perturbation margin may be more constrained for larger disturbances and for larger parametric uncertainties. Working in an L2 setting, and within the framework of the nonlinear gap metric, universal adaptive controllers are first given achieving stabilisation for first order nominal plants, and the results are then generalised to relative degree one nominal plants. Necessary asymptotic properties of the robustness margins are derived for the class of controllers considered. Extensions to the Linfty setting are also developed where two alternative designs are given. A notion of a semi universal control design is introduced, which is the property that a bound on performance exists which is independent of the a-priori known uncertainty level, and a characterisation is given for when semi-universal designs outperform the class of memoryless controllers and the class of LTI controllers. Robust semi-universal adaptive control designs are given for nominal plants under the classical assumptions of adaptive control in both the L2 and Linfty settings. The results are applied throughout to explicit classes of unmodelled dynamics including the Rohrs example.

PDF gap050420.pdf - Other
Download (411kB)

Citation

French, M. (2008) Adaptive control and robustness in the gap metric IEEE Transactions on Automatic Control, 53, (2), pp. 461-478. (doi:10.1109/TAC.2008.916659).

More information

Published date: March 2008
Additional Information: This version April 2005
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 260787
URI: http://eprints.soton.ac.uk/id/eprint/260787
ISSN: 0018-9286
PURE UUID: f893cca4-7171-4aef-8d6e-4bde52eda57d

Catalogue record

Date deposited: 21 Apr 2005
Last modified: 18 Jul 2017 09:09

Export record

Altmetrics

Contributors

Author: M. French

University divisions


Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×