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. Technical Report. California Institute of Technology. [CaltechCDSTR:1995.CIT-CDS-95-012]

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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 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.

EPrint Type:	Monograph (Technical Report)
Subjects:	All Records
ID Code:	18
Deposited By:	Richard M. Murray
Deposited On:	18 October 2002
Unique Identifier:	CaltechCDSTR:1995.CIT-CDS-95-012
Official 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.

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