Singularly Perturbed Systems of Diffusion Type and Feedback Control

  • A. van Harten
Part of the International Centre for Mechanical Sciences book series (CISM, volume 280)


In this paper we shall consider linear systems of diffusion-type subject to a certain feed-back control mechanism in a situation, where the diffusion constant is a small parameter. Such controlled diffusion systems can be found f.e. in the context of heating problems [1], [2] or chemical or nuclear reactor design, [3]. For the feedback control there are many possibilities: feedback without òr with memory, with distributed input òr input through the boundary, etc., while it also depends on the number and kind of observations, cf. [2], [4], [5], [17]. Here we shall consider distributed as well as boundary control, but always on the basis of an instantaneous feedback coupling using observations of the state in a finite number of points y1,...,yp in the interior of the domain D. In the case of Dirichlet boundary conditions the evolution of the state is described by one of the following problems:


Feedback Control Control Operator Singular Perturbation Boundary Control Analytic Semigroup 
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Copyright information

© Springer-Verlag Wien 1983

Authors and Affiliations

  • A. van Harten
    • 1
  1. 1.Mathematical InstituteUn. of UtrechtThe Netherlands

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