Optimal actuator location for time and norm optimal control of null controllable heat equation

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• 作者：Bao-Zhu Guo (1) (2) (3)
  Dong-Hui Yang (4)
  
  1. Academy of Mathematics and Systems Science ; Academia Sinica ; Beijing聽 ; 100190 ; People鈥檚 Republic of China
  2. School of Computational and Applied Mathematics ; University of the Witwatersrand ; Wits 2050 ; Johannesburg ; South Africa
  3. Department of Mathematics ; King Abdulaziz University ; Jeddah聽 ; 21589 ; Saudi Arabia
  4. School of Mathematics and Statistics ; Central South University ; Changsha聽 ; 410075 ; People鈥檚 Republic of China
  
• 关键词：Heat equation ; Optimal control ; Shape optimization
• 刊名：Mathematics of Control, Signals, and Systems (MCSS)
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：27
• 期：1
• 页码：23-48
• 全文大小：308 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Communications Engineering and Networks
  Control Engineering
  
• 出版者：Springer London
• ISSN：1435-568X

文摘

We consider minimal time and minimal norm of the optimal controls for a multi-dimensional internally controlled heat equation with control domain varying over a class of open sets. Two problems are formulated separately into different types of shape optimization problems over this open set class. The governing equation with any given initial value and admissible control are considered as constraints, and minimal time or minimal norm of the optimal controls is considered as cost for related shape optimization. The solution of the shape optimization leads to the optimal actuator location for optimal controls. The existence of such an optimal location domain for both minimal time and minimal norm controls is presented. A different problem that relates the balance between minimal time and minimal norm controls is also discussed. This study builds a link between optimal control and shape optimization for this multi-dimensional heat equation.