Optimal control of affine connection control systems from the point of view of Lie algebroids

TL;DR

This paper employs Lie algebroid theory to analyze optimal control problems for affine connection control systems on Lie groups, providing a geometric characterization of critical trajectories as Hamiltonian vector fields.

Contribution

It introduces a Lie algebroid framework to study optimal control problems on Lie groups, offering a geometric perspective on critical trajectories.

Findings

Critical trajectories are characterized as Hamiltonian vector fields.

The framework provides a geometric interpretation of optimal control solutions.

Application to affine connection control systems on Lie groups.

Abstract

The purpose of this paper is to use the framework of Lie algebroids to study optimal control problems for affine connection control systems on Lie groups. In this context, the equations for critical trajectories of the problem are geometrically characterized as a Hamiltonian vector field.