Lie Algebroids in Classical Mechanics and Optimal Control
Eduardo Martinez
TL;DR
This paper reviews recent developments in the theory of Lagrangian and optimal control systems on Lie algebroids, focusing on symplectic formalism, reduction techniques, and the Pontryagin maximum principle.
Contribution
It introduces new methods for reducing optimal control problems on Lie algebroids and extends classical mechanics formalism to this geometric framework.
Findings
Development of a reduction procedure for Pontryagin's maximum principle on Lie algebroids
Extension of symplectic and variational formalisms to Lie algebroid systems
New insights into the geometric structure of Lagrangian systems on Lie algebroids
Abstract
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.
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