Geometric reduction in optimal control theory with symmetries

TL;DR

This paper explores how symmetries in optimal control systems can be exploited to simplify analysis and solutions through geometric reduction techniques, extending classical results to both regular and singular cases.

Contribution

It develops a comprehensive geometric framework for symmetry reduction in optimal control, including a presymplectic approach and an adaptation of Noether's theorem.

Findings

Unified reduction procedure for regular and singular systems

Extension of Noether's theorem to presymplectic optimal control

Application of Marsden-Weinstein reduction in control context

Abstract

A general study of symmetries in optimal control theory is given, starting from the presymplectic description of this kind of system. Then, Noether's theorem, as well as the corresponding reduction procedure (based on the application of the Marsden-Weinstein theorem adapted to the presymplectic case) are stated both in the regular and singular cases, which are previously described.