A Short Proof of the Pontryagin Maximum Principle on Manifolds

Dong Eui Chang

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arXiv · 0905.1888

A Short Proof of the Pontryagin Maximum Principle on Manifolds

Dong Eui Chang

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Abstract

Applying the Tubular Neighborhood Theorem, we give a short and new proof of the Pontryagin Maximum Principle on a smooth manifold. The idea is as follows. Given a control system on a manifold $M$, we embed it into an open subset of some $\mathbb R^n$, and extend the control system to the open set. Then, we apply the Pontryagin Maximum Principle on $\mathbb R^n$ to the extended system and project the consequence to $M$.

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Dong Eui Chang. 2009-05-12. A Short Proof of the Pontryagin Maximum Principle on Manifolds. https://arxiv.org/abs/0905.1888

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