A finite-dimensional asymptotic observer for a class of distributed parameter systems
作者:
NOBUO FUJII,
MASAHIDE HIRAI,
期刊:
International Journal of Control
(Taylor Available online 1980)
卷期:
Volume 32,
issue 6
页码: 951-962
ISSN:0020-7179
年代: 1980
DOI:10.1080/00207178008922901
出版商: Taylor & Francis Group
数据来源: Taylor
摘要:
A finite-dimensional asymptotic observer is derived on the basis of a Calcrkin approximation for a class of distributed parameter systems. The systems are described by a partial differential equation of parabolic type. The measured outputs are assumed to be obtained through a finite number of sensors located in the interior. The sensor influence functions are added to the usual basis for the Galerkin approximation and Schmidt's orthogonalization is performed to yield a new basis. The Galerkin approximate solution is sought in terms of this basis. By this procedure the observation spillover problem is overcome. Moreover, in view of the fact that it is generally difficult to obtain the closed-form expressions for the eigenfunctions of the equation, the method is useful for practical substantiation of the observer. The uniform convergence of the Galerkin approximate sequence for the partial differential equation is proved and used to ensure the convergence of the estimated state in a somewhat stronger sense. A numerical example is given which illustrates the power of the method.
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