A simple proof of the Pontryagin maximum principle on manifolds

作者：Chang Dong Eui^*

来源：Automatica, 2011, 47(3): 630-633.

DOI：10.1016/j.automatica.2011.01.037

• Optimal control
• Pontryagin maximum principle
• Tubular neighborhood
• Whitney embedding

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.

• 出版日期2011-3