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Exponential Stabilization of Driftless Nonlinear Control Systems using Homogeneous Feedback

M'Closkey, Robert T. and Murray, Richard M. (1995) Exponential Stabilization of Driftless Nonlinear Control Systems using Homogeneous Feedback. California Institute of Technology . (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-012

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Use this Persistent URL to link to this item: http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-012

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 non-standard dilation that is compatible with the algebraic structure of the control Lie algebra. Using this structure, we show that any continuous, time-varying controller that achieves exponential stabilization 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:Report or Paper (Technical Report)
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1995.CIT-CDS-95-012
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-012
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28017
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:18 Oct 2002
Last Modified:26 Dec 2012 14:28

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