Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 673013, 16 pages
doi:10.1155/2010/673013
Research Article

Optimal Control of Linear Impulsive Antiperiodic Boundary Value Problem on Infinite Dimensional Spaces

JinRong Wang1 and YanLong Yang2

1College of Science, Guizhou University, Guiyang, Guizhou 550025, China
2College of Technology, Guizhou University, Guiyang, Guizhou 550004, China

Received 14 July 2009; Accepted 9 February 2010

Academic Editor: Binggen Zhang

Copyright © 2010 JinRong Wang and YanLong Yang. 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

A class of optimal control problems for infinite dimensional impulsive antiperiodic boundary value problem is considered. Using exponential stabilizability and discussing the impulsive evolution operators, without compactness and exponential stability of the semigroup governed by original principle operator, we present the existence of optimal controls. At last, an example is given for demonstration.