# Pontryagin Maximum Principle and Stokes Theorem

## TL;DR

This paper introduces a geometric approach to optimal control problems using Stokes Theorem, providing a new derivation of the Pontryagin Maximum Principle and suggesting potential generalizations.

## Contribution

A novel geometric unfolding of the Mayer problem that derives the Pontryagin Maximum Principle through Stokes Theorem, offering new insights and generalizations.

## Key findings

- Derivation of Pontryagin Maximum Principle via Stokes Theorem
- New geometric characterization of optimal solutions
- Potential for extending classical control principles

## Abstract

We present a new geometric unfolding of a prototype problem of optimal control theory, the Mayer problem. This approach is crucially based on the Stokes Theorem and yields to a necessary and sufficient condition that characterizes the optimal solutions, from which the classical Pontryagin Maximum Principle is derived in a new insightful way. It also suggests generalizations in diverse directions of such famous principle.