A Short Proof of the Pontryagin Maximum Principle on Manifolds

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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References in corpus (1)

• Geometric Approach to Pontryagin's Maximum Principle