Advances in Difference Equations
Volume 2011 (2011), Article ID 385324, 16 pages
doi:10.1155/2011/385324
Research Article

Study of an Approximation Process of Time Optimal Control for Fractional Evolution Systems in Banach Spaces

JinRong Wang1 and Yong Zhou2

1Department of Mathematics, Guizhou University, Guiyang, Guizhou 550025, China
2Department of Mathematics, Xiangtan University, Xiangtan, Hunan 411105, China

Received 1 October 2010; Accepted 9 December 2010

Academic Editor: J. J. Trujillo

Copyright © 2011 JinRong Wang and Yong 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 paper is devoted to the study of an approximation process of time optimal control for fractional evolution systems in Banach spaces. We firstly convert time optimal control problem into Meyer problem. By virtue of the properties of the family of solution operators given by us, the existence of optimal controls for Meyer problem is proved. Secondly, we construct a sequence of Meyer problems to successive approximation of the original time optimal control problem. Finally, a new approximation process is established to find the solution of time optimal control problem. Our method is different from the standard method.