American Institute of Mathematical Sciences

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November  2007, 8(4): 925-941. doi: 10.3934/dcdsb.2007.8.925

On the existence of time optimal controls for linear evolution equations

Kim Dang Phung 1, , Gengsheng Wang 2, and  Xu Zhang 3,

1. 

Yangtze Center of Mathematics, Sichuan University, Chengdu 610064, China
2. 

School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
3. 

Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100190, China

Received  November 2006 Revised  May 2007 Published  August 2007

This work concerns with the existence of the time optimal controls for some linear evolution equations without the a priori assumption on the existence of admissible controls. Both global and local existence results are presented. Some necessary conditions, sufficient conditions, and necessary and sufficient conditions for the existence of time optimal controls are derived by establishing the relationship between controllability and time optimal control problems.
Keywords: evolution equation, admissible control, Time optimal control, constrained controllability..
Mathematics Subject Classification: Primary: 49J20; Secondary: 93B05, 35B3.
Citation: Kim Dang Phung, Gengsheng Wang, Xu Zhang. On the existence of time optimal controls for linear evolution equations. Discrete and Continuous Dynamical Systems - B, 2007, 8 (4) : 925-941. doi: 10.3934/dcdsb.2007.8.925
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