From exact observability to identification of singular sources
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- 作者：Marius Tucsnak (1)
George Weiss (2)
1. Institut Elie Cartan ; Universit茅 de Lorraine ; 54506聽 ; Vandoeuvre-l茅s-Nancy ; France
2. Department of EE-Systems ; Tel Aviv University ; 69978聽 ; Ramat Aviv ; Israel - 关键词：Exact observability ; Inverse problems ; Point sources ; Wave equation ; Exact controllability
- 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：1-21
- 全文大小：255 KB
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- 刊物主题：Mathematics
Mathematics
Communications Engineering and Networks
Control Engineering - 出版者：Springer London
- ISSN：1435-568X
文摘
We give general results about the identifiability of source terms for infinite-dimensional linear systems that are exactly observable. We allow the source term to be unbounded, i.e., not contained in the state space, but in one of a sequence of extended spaces. We show that the operator from the source term to the output function is bounded from below, in suitable norms. We apply the main result to a system described by the wave equation in a bounded \(n\) -dimensional domain. We derive results of independent interest concerning the range of the input map of an exactly controllable system, when restricted to various spaces of smooth input functions.