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

David González-Sánchez, Onésimo Hernández-Lerma
2013 Journal of Dynamics & Games  
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)
more » ... everal (discounted) stationary and nonstationary control problems. 2010 Mathematics Subject Classification. Primary: 93C55, 91B55, 93E20. 57 58 DAVID GONZÁLEZ-SÁNCHEZ AND ONÉSIMO HERNÁNDEZ-LERMA each t = 0, 1, 2, . . .. The optimal control problem (OCP) is to find a policy {u t } that maximizes (2). To illustrate these concepts we next present an example.
doi:10.3934/jdg.2014.1.57 fatcat:stepjj5omfccvdw2jpmtsburm4