On the Euler equation approach to discrete--time nonstationary optimal control problems
David González-Sánchez - Departamento de Matemáticas, Instituto Tecnológico Autónomo de México (ITAM), Río Hondo 1, México D.F. 01000, 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.
Received: April 2012; Revised: March 2013; Available Online: June 2013.