A simple proof of the Pontryagin maximum principle on manifolds

Abstract

Applying the tubular neighborhood theorem, we give a simple 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 some R-n and extend the control system to R-n. Then, we apply the Pontryagin maximum principle on R-n to the extended system and project the consequence to M. (C) 2011 Elsevier Ltd. All rights reserved.