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IMA Journal of Mathematical Control and Information 2004 21(4):457-492; doi:10.1093/imamci/21.4.457
© 2004 by Institute of Mathematics and its Applications
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Mechanical control systems on Lie algebroids

Jorge Cortés1,* and Eduardo Martínez2,§

1 Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, 1308 W Main St, Urbana, IL 61801, USA, 2 Departamento de Matemática Aplicada, Universidad de Zaragoza 50009 Zaragoza, Spain

This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and non-holonomic constraints, mechanical systems with symmetry and mechanical systems evolving on semidirect products. We introduce the notions of linear connection, symmetric product and geodesically invariant subbundle on a Lie algebroid. We present appropriate tests for various notions of accessibility and controllability, and analyse the relation between the controllability properties of control systems related by a morphism of Lie algebroids.

Keywords: mechanical control systems; Lie algebroids, nonlinear controllability.

Received 11 September 2003.

* Email: jcortes{at}uiuc.edu

§ Email: emf{at}unizar.es


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