Contact Geometry of the Pontryagin Maximum Principle

TL;DR

This paper explores the Pontryagin maximum principle through contact geometry, providing geometric interpretations of its core concepts and deriving the transversality condition more simply.

Contribution

It introduces a contact-geometric framework for the Pontryagin maximum principle, offering new insights and a streamlined derivation of the transversality condition.

Findings

Contact geometry offers natural interpretations of key PMP notions.

The framework simplifies the derivation of the transversality condition.

Provides a unified geometric perspective on optimal control principles.

Abstract

This paper gives a brief contact-geometric account of the Pontryagin maximum principle. We show that key notions in the Pontryagin maximum principle---such as the separating hyperplanes, costate, necessary condition, and normal/abnormal minimizers---have natural contact-geometric interpretations. We then exploit the contact-geometric formulation to give a simple derivation of the transversality condition for optimal control with terminal cost.