G2TT
来源类型Book Section
DOI10.1007/BFb0043188
Topological properties of observability for a system of parabolic type.
Miyamoto S; Byrnes, C.I.; Kurzhanski, A.B.
发表日期1988
出处Modelling and Adaptive Control. Eds. Byrnes, C.I. & Kurzhanski, A.B. , pp. 239-253 Germany: Springer Berlin/Heidelberg. ISBN 978-3-540-38904-0 DOI: 10.1007/BFb0043188 .
出版年1988
语种英语
摘要The purpose of the present paper is to demonstrate topological properties of observable regions in a distributed parameter system. A parabolic partial differential equation with constant coefficients is considered. According to Sakawa's definition, observability is defined to be the possibility of the unique determination of the initial value by point measurements, or by spatially averaged measurements. Furthermore, n-mode observability is defined to be the possibility of the unique determination of the coefficients corresponding to the first n eigenvalues, based on the expansion of the solution by eigenfunctions. Then it is proved that n-mode observability is generic, that is, open and dense, whereas observability is shown to be dense in the whole space of measurements. In case of point measurements, it is shown that observability is valid almost everywhere with respect to the Lebesque measure. Moreover genericity of n-mode controllability and the related properties of controllability will be shown for the dual systems with controls.
主题System and Decision Sciences - Core (SDS)
URLhttp://pure.iiasa.ac.at/id/eprint/13001/
来源智库International Institute for Applied Systems Analysis (Austria)
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资源类型智库出版物
条目标识符http://119.78.100.153/handle/2XGU8XDN/133148
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Miyamoto S,Byrnes, C.I.,Kurzhanski, A.B.. Topological properties of observability for a system of parabolic type.. 1988.
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