dc.contributor.author | Mueller, Markus | |
dc.contributor.author | Ilchmann, Achim | |
dc.date.accessioned | 2015-08-19T11:08:01Z | |
dc.date.issued | 2009-12 | |
dc.description.abstract | For m-input, m-output, finite-dimensional, linear systems satisfying the classical assumptions of adaptive control (i.e., (i) minimum phase, (ii) relative degree one and (iii) positive definite high-frequency gain matrix), two control strategies are considered: the well-known λ-tracking and funnel control. An application of the λ-tracker to systems satisfying (i)–(iii) yields that all states of the closed-loop system are bounded and |e| is ultimately bounded by some prespecified λ > 0. An application of the funnel controller achieves tracking of the error e within a prescribed performance funnel if applied to linear systems satisfying (i)–(iii). Moreover, all states of the closed-loop system are bounded. The funnel boundary can be chosen from a large set of functions. Invoking the conceptual framework of the nonlinear gap metric, we show that the λ-tracker and the funnel controller are robust. In the present setup this means in particular that λ-tracking and funnel control copes with bounded input and output disturbances and, more importantly, may be applied to any system which is “close” (in terms of a “small” gap) to a system satisfying (i)–(iii), and which may not satisfy any of the classical conditions (i)–(iii), as long as the initial conditions and the disturbances are “small”. | en_GB |
dc.identifier.citation | Proceedings of the 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference pp. 638 - 643 | en_GB |
dc.identifier.uri | http://hdl.handle.net/10871/18076 | |
dc.language.iso | en | en_GB |
dc.publisher | Institute of Electrical and Electronics Engineers (IEEE) | en_GB |
dc.title | Robustness of λ-tracking and funnel control in the gap metric | en_GB |
dc.type | Conference proceedings | en_GB |
dc.date.available | 2015-08-19T11:08:01Z | |
dc.identifier.isbn | 978-1-4244-3872-3 | |
dc.identifier.issn | 0191-2216 | |
dc.description | Published | en_GB |
dc.description | Copyright © 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. | en_GB |
dc.description | Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on 15-18 December 2009 | en_GB |