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 (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1995.CIT-CDS-95-012
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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|
|Usage Policy:||You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.|
|Deposited By:||Imported from CaltechCDSTR|
|Deposited On:||18 Oct 2002|
|Last Modified:||26 Dec 2012 14:28|
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