A biased approach to nonlinear robust stability and
performance with applications to adaptive control
A biased approach to nonlinear robust stability and
performance with applications to adaptive control
The nonlinear robust stability theory of Georgiou and Smith [IEEE Trans. Automat. Control, 42 (1997), pp. 1200–1229] is generalized to the case of notions of stability with bias terms. An example from adaptive control illustrates nontrivial robust stability certificates for systems which the previous unbiased theory could not establish a nonzero robust stability margin. This treatment also shows that the bounded-input bounded-output robust stability results for adaptive controllers in French [IEEE Trans. Automat. Control, 53 (2008), pp. 461–478] can be refined to show preservation of biased forms of stability under gap perturbations. In the nonlinear setting, it also is shown that in contrast to linear time invariant systems, the problem of optimizing nominal performance is not equivalent to maximizing the robust stability margin.
gap metric, robust stability, nonlinear systems, adaptive control
1220-1243
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8
Bian, Wenming
7fed6a6f-4242-4fdb-9096-cbf73a7d96fc
22 May 2012
French, Mark
22958f0e-d779-4999-adf6-2711e2d910f8
Bian, Wenming
7fed6a6f-4242-4fdb-9096-cbf73a7d96fc
French, Mark and Bian, Wenming
(2012)
A biased approach to nonlinear robust stability and
performance with applications to adaptive control.
SIAM Journal on Control and Optimization, 50 (3), .
(doi:10.1137/10078726X).
Abstract
The nonlinear robust stability theory of Georgiou and Smith [IEEE Trans. Automat. Control, 42 (1997), pp. 1200–1229] is generalized to the case of notions of stability with bias terms. An example from adaptive control illustrates nontrivial robust stability certificates for systems which the previous unbiased theory could not establish a nonzero robust stability margin. This treatment also shows that the bounded-input bounded-output robust stability results for adaptive controllers in French [IEEE Trans. Automat. Control, 53 (2008), pp. 461–478] can be refined to show preservation of biased forms of stability under gap perturbations. In the nonlinear setting, it also is shown that in contrast to linear time invariant systems, the problem of optimizing nominal performance is not equivalent to maximizing the robust stability margin.
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120111robustbias.pdf
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Published date: 22 May 2012
Keywords:
gap metric, robust stability, nonlinear systems, adaptive control
Organisations:
Southampton Wireless Group
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Local EPrints ID: 339659
URI: http://eprints.soton.ac.uk/id/eprint/339659
PURE UUID: 65c7dd07-577b-4395-a928-992b78ac811d
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Date deposited: 29 May 2012 09:23
Last modified: 14 Mar 2024 11:13
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Author:
Mark French
Author:
Wenming Bian
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