Numerical Algebra, Control and Optimization (NACO)

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

Pages: 161 - 173, Volume 3, Issue 1, March 2013      doi:10.3934/naco.2013.3.161

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Hans Josef Pesch - University of Bayreuth, Chair of Mathematics in Engineering Sciences, Bayreuth, D 95440, Germany (email)

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.

Received: January 2012;      Revised: November 2012;      Available Online: January 2013.