Journal Article

Mechanical control systems on Lie algebroids

Jorge Cortés and Eduardo Martínez

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 21, issue 4, pages 457-492
Published in print December 2004 | ISSN: 0265-0754
Published online December 2004 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/21.4.457
Mechanical control systems on Lie algebroids

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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

Journal Article.  0 words. 

Subjects: Mathematics

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