Some applications of quasi-velocities in optimal control

Details Some applications of quasi-velocities in optimal control Some applications of quasi-velocities in optimal control

2011-02-10

arxiv.org/abs/1102.2203v1

Mathematics

Optimization and Control

Revtex 4.1, 20 pages. To appear in Int. J. Geom. Meth. Modern Physics

Scientific paper

In this paper we study optimal control problems for nonholonomic systems defined on Lie algebroids by using quasi-velocities. We consider both kinematic, i.e. systems whose cost functional depends only on position and velocities, and dynamic optimal control problems, i.e. systems whose cost functional depends also on accelerations. The formulation of the problem directly at the level of Lie algebroids turns out to be the correct framework to explain in detail similar results appeared recently (Maruskin and Bloch, 2007). We also provide several examples to illustrate our construction.

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