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来源类型 | Book Section |
DOI | 10.1007/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) |
URL | http://pure.iiasa.ac.at/id/eprint/13001/ |
来源智库 | International Institute for Applied Systems Analysis (Austria) |
引用统计 | |
资源类型 | 智库出版物 |
条目标识符 | http://119.78.100.153/handle/2XGU8XDN/133148 |
推荐引用方式 GB/T 7714 | Miyamoto S,Byrnes, C.I.,Kurzhanski, A.B.. Topological properties of observability for a system of parabolic type.. 1988. |
条目包含的文件 | 条目无相关文件。 |
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