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Exponential stabilization of driftless nonlinear control systems using homogeneous feedback

M'Closkey, Robert T. and Murray, Ruchard M. (1997) Exponential stabilization of driftless nonlinear control systems using homogeneous feedback. IEEE Transactions on Automatic Control, 42 (5). pp. 614-628. ISSN 0018-9286. http://resolver.caltech.edu/CaltechAUTHORS:MCLieeetac97

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Abstract

This paper focuses on the problem of exponential stabilization of controllable, driftless systems using time-varying, homogeneous feedback. The analysis is performed with respect to a homogeneous norm in a nonstandard dilation that is compatible with the algebraic structure of the control Lie algebra. It can be shown that any continuous, time-varying controller that achieves exponential stability relative to the Euclidean norm is necessarily non-Lipschitz. Despite these restrictions, we provide a set of constructive, sufficient conditions for extending smooth, asymptotic stabilizers to homogeneous, exponential stabilizers. The modified feedbacks are everywhere continuous, smooth away from the origin, and can be extended to a large class of systems with torque inputs. The feedback laws are applied to an experimental mobile robot and show significant improvement in convergence rate over smooth stabilizers.


Item Type:Article
Additional Information:© Copyright 1997 IEEE. Reprinted with permission. Manuscript received May 19, 1995; revised August 16, 1996 and November 8, 1996. Recommended by Associate Editor, J.-B. Pomet. The authors would like to thank L. Praly and the reviewers for their thoughtful comments.
Subject Keywords:Dilation, driftless, exponential stabilization, homogeneous, nonholonomic
Record Number:CaltechAUTHORS:MCLieeetac97
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:MCLieeetac97
Alternative URL:http://dx.doi.org/10.1109/9.580865
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7316
Collection:CaltechAUTHORS
Deposited By: Archive Administrator
Deposited On:29 Jan 2007
Last Modified:26 Dec 2012 09:30

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