Optimal control problems on the co-adjoint Lie groupoids

TL;DR

This paper investigates invariant optimal control problems on Lie groupoids, demonstrating their reduction to co-adjoint Lie algebroids and illustrating the theory with an example.

Contribution

It introduces a reduction method for invariant optimal control problems on Lie groupoids to their co-adjoint Lie algebroids, providing a new theoretical framework.

Findings

Reduction of invariant control problems to co-adjoint Lie algebroids

Theoretical framework for control problems on Lie groupoids

Illustrative example demonstrating the concepts

Abstract

In this work we study the invariant optimal control problem on Lie groupoids. We show that any invariant optimal control problem on a Lie groupoid reduces to its co-adjoint Lie algebroid. In the final section of the paper, we present an illustrative example.