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Dissipation and Controlled Euler-Poincaré Systems

Woolsey, C. A. and Bloch, A. M. and Leonard, N. E. and Marsden, J. E. (2001) Dissipation and Controlled Euler-Poincaré Systems. In: Proceedings of the 40th IEEE Conference on Decision and Control, 2001. Vol.4. IEEE , Piscataway, NJ, pp. 3378-3383. ISBN 0780370619.

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The method of controlled Lagrangians is a technique for stabilizing underactuated mechanical systems which involves modifying a system’s energy and dynamic structure through feedback. These modifications can obscure the effect of physical dissipation in the closed-loop. For example, generic damping can destabilize an equilibrium which is closed-loop stable for a conservative system model. In this paper, we consider the effect of damping on Euler-Poincaré (special reduced Lagrangian) systems which have been stabilized about an equilibrium using the method of controlled Lagrangians. We describe a choice of feed-back dissipation which asymptotically stabilizes a sub-class of controlled Euler-Poincaré systems subject to physical damping. As an example, we consider intermediate axis rotation of a damped rigid body with a single internal rotor.

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Additional Information:© 2001 IEEE. The authors thank Dong Eui Chang for helpful comments. We acknowledge partial support from the NSF, ONR and AFOSR.
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Subject Keywords:Lie groups , Lyapunov methods , asymptotic stability , closed loop systems , damping , feedback
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INSPEC Accession Number7212201
Record Number:CaltechAUTHORS:20101025-103909189
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:20500
Deposited By: Ruth Sustaita
Deposited On:30 Nov 2010 18:45
Last Modified:09 Nov 2021 00:00

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