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Lyapunov constraints and global asymptotic stabilization

Grillo, Sergio and Marsden, Jerrold and Nair, Sujit (2011) Lyapunov constraints and global asymptotic stabilization. Journal of Geometric Mechanics, 3 (2). pp. 145-196. ISSN 1941-4889. https://resolver.caltech.edu/CaltechAUTHORS:20110823-142822793

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Abstract

In this paper, we develop a method for stabilizing underactuated mechanical systems by imposing kinematic constraints (more precisely Lyapunov constraints). If these constraints can be implemented by actuators, i.e., if there exists a related constraint force exerted by the actuators, then the existence of a Lyapunov function for the system under consideration is guaranteed. We establish necessary and sufficient conditions for the existence and uniqueness of constraint forces. These conditions give rise to a system of PDEs whose solution is the required Lyapunov function. To illustrate our results, we solve these PDEs for certain underactuated mechanical systems of interest such as the inertia wheel-pendulum, the inverted pendulum on a cart system and the ball and beam system.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.3934/jgm.2011.3.145DOIUNSPECIFIED
http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=6361PublisherUNSPECIFIED
Additional Information:© 2011 American Institute of Mathematical Sciences. Received: October 2010; Revised: June 2011; Published: July 2011. Communicated by Manuel de León. S. Grillo thanks CONICET and Fulbright Commission for their financial support and the personnel at the Control and Dynamical Systems department at Caltech for their kind hospitality.
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Funding AgencyGrant Number
CONICET UNSPECIFIED
Fulbright CommissionUNSPECIFIED
Subject Keywords:Lagrangian and Hamiltonian systems; nonlinear control; energy shaping
Issue or Number:2
Classification Code:Mathematics Subject Classification: Primary: 93D20; Secondary: 53Z05
Record Number:CaltechAUTHORS:20110823-142822793
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20110823-142822793
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:24997
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:24 Aug 2011 18:49
Last Modified:03 Oct 2019 03:01

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