Carath&#233odory's royal road of the calculus of variations:       Missed exits to the maximum principle of optimal control theory

Hans Josef Pesch

doi:10.3934/naco.2013.3.161

Article Contents

2013, Volume 3, Issue 1: 161-173. Doi: 10.3934/naco.2013.3.161

This issue Previous Article Necessary optimality conditions for infinite horizon variational problems on time scales Next Article Incremental quadratic stability

Carathéodory's royal road of the calculus of variations: Missed exits to the maximum principle of optimal control theory

Hans Josef Pesch^1,

1.
University of Bayreuth, Chair of Mathematics in Engineering Sciences, Bayreuth, D 95440

Received: January 2012

Revised: November 2012

Published: December 2012

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Abstract

The purpose of the present paper is to show that the most prominent results in optimal control theory, the distinction between state and control variables, the maximum principle, and the principle of optimality, resp. Bellman's equation are immediate consequences of Carathéodory's achievements published about two decades before optimal control theory saw the light of day.

Keywords:

History of calculus of variations and optimal control,
royal road of calculus of variations,
Bellman equation,
maximum principle,
Carathéodory.

Mathematics Subject Classification: Primary: 01A60, 49-03; Secondary: 90-03, 91-03.

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