Journal of Dynamics and Games (JDG)

On the Euler equation approach to discrete--time nonstationary optimal control problems

Pages: 57 - 78, Volume 1, Issue 1, January 2014      doi:10.3934/jdg.2014.1.57

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David González-Sánchez - Departamento de Matemáticas, Instituto Tecnológico Autónomo de México (ITAM), Río Hondo 1, México D.F. 01000, Mexico (email)
Onésimo Hernández-Lerma - Mathematics Department, CINVESTAV-IPN, A. Postal 14-740, México D.F. 07000, Mexico (email)

Abstract: We are concerned with deterministic and stochastic nonstationary discrete--time optimal control problems in infinite horizon. We show, using Gâteaux differentials, that the so--called Euler equation and a transversality condition are necessary conditions for optimality. In particular, the transversality condition is obtained in a more general form and under milder hypotheses than in previous works. Sufficient conditions are also provided. We also find closed--form solutions to several (discounted) stationary and nonstationary control problems.

Keywords:  Discrete--time control systems, time--varying systems, infinite horizon, Euler equation, transversality condition.
Mathematics Subject Classification:  Primary: 93C55, 91B55, 93E20.

Received: April 2012;      Revised: March 2013;      Available Online: June 2013.