Abstract and Applied Analysis
Volume 2013 (2013), Article ID 791786, 14 pages
http://dx.doi.org/10.1155/2013/791786
Research Article

Infinite Horizon Optimal Control of Stochastic Delay Evolution Equations in Hilbert Spaces

Xueping Zhu1 and Jianjun Zhou2

1School of Astronautics, Northwestern Polytechnical University, Xi'an, Shaanxi 710072, China
2College of Science, Northwest A&F University, Yangling, Shaanxi 712100, China

Received 6 September 2012; Accepted 16 December 2012

Academic Editor: Juan J. Trujillo

Copyright © 2013 Xueping Zhu and Jianjun Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The aim of the present paper is to study an infinite horizon optimal control problem in which the controlled state dynamics is governed by a stochastic delay evolution equation in Hilbert spaces. The existence and uniqueness of the optimal control are obtained by means of associated infinite horizon backward stochastic differential equations without assuming the Gâteaux differentiability of the drift coefficient and the diffusion coefficient. An optimal control problem of stochastic delay partial differential equations is also given as an example to illustrate our results.