Mechanical control systems on Lie algebroids

Details Mechanical control systems on Lie algebroids Mechanical control systems on Lie algebroids

2004-02-26

arxiv.org/abs/math/0402437v1

IMA Journal of Mathematical Control and Information 21 (4) (2004), 457-492

Mathematics

Optimization and Control

29 pages, no figures. To appear in IMA Journal of Mathematical Control and Information

Scientific paper

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 nonholonomic 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 analyze the relation between the controllability properties of control systems related by a morphism of Lie algebroids.

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