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Optimal Control Theory on almost-Lie Algebroids

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arxiv 1111.1549 v1 pith:ES3XQJIA submitted 2011-11-07 math.OC math.DG

Michal Jozwikowski This is my paper · ORCID
classification math.OCmath.DG
keywords algebroidsconditionsgeneralocpsalmost-lieboundarycontroloptimal
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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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Cited by 1 Pith paper

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  1. Optimal control problems on the co-adjoint Lie groupoids

    math.OC 2024-11 reject novelty 3.0 of 10

    Any right-invariant optimal control problem on a Lie groupoid is claimed to reduce to one on its co-adjoint Lie algebroid, but the key step is cited, not proven.

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