A Short Proof of the Pontryagin Maximum Principle on Manifolds

2009/05/12 by Dong Eui Chang, Chang, Dong Eui
Computer Science · Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.0905.1888

openalex publication_date 2009/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Rⁿ, and extend the control system to the open set. Then, we apply the Pontryagin Maximum Principle on \mathbb Rⁿ to the extended system and project the consequence to M.

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