Open Access

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

Advances in Difference Equations20102011:385324

https://doi.org/10.1155/2011/385324

Received: 1 October 2010

Accepted: 9 December 2010

Published: 14 December 2010

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.

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Authors’ Affiliations

(1)
Department of Mathematics, Guizhou University
(2)
Department of Mathematics, Xiangtan University

Copyright

© JinRong Wang and Yong Zhou. 2011

This article is published under license to BioMed Central Ltd. 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.