Optimal Control Theory on almost-Lie Algebroids

Details Optimal Control Theory on almost-Lie Algebroids Optimal Control Theory on almost-Lie Algebroids

2011-11-07

arxiv.org/abs/1111.1549v1

Mathematics

Optimization and Control

PhD thesis, 122 pages, with index

Scientific paper

We extend the Pontryagin Maximum Principle (PMP) to the geometric setting of almost-Lie (AL) algebroids -- objects which generalize Lie algebroids. The result may be understood as a very general reduction scheme for optimal control problems (OCPs). It covers the standard PMP, as well as gives necessary optimality conditions for symmetric OCPs on Lie groups, principal bundles, and Lie groupoids. We do not assume the symmetry of boundary conditions. The ideas are based on a very general concept of homotopy of admissible paths on AL algebroids. Our framework works for OCPs with fixed-end-points and general boundary conditions.

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