A contact covariant approach to optimal control with applications to sub-Riemannian geometry

TL;DR

This paper introduces a contact geometric framework for optimal control problems, offering new characterizations of sub-Riemannian extremals that enhance understanding and analysis of such systems.

Contribution

It provides a novel contact covariant approach to optimal control, expanding on previous work to characterize extremals in sub-Riemannian geometry.

Findings

Characterization of normal sub-Riemannian extremals

Characterization of abnormal sub-Riemannian extremals

Simplified geometric descriptions of extremals

Abstract

We discuss contact geometry naturally related with optimal control problems (and Pontryagin Maximum Principle). We explore and expand the observations of [Ohsawa, 2015], providing simple and elegant characterizations of normal and abnormal sub-Riemannian extremals.