Journal Article

Approximate parametric optimization of infinite-dimensional systems

PIOTR GRABOWSKI

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 16, issue 2, pages 115-123
Published in print June 1999 | ISSN: 0265-0754
Published online June 1999 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/16.2.115
Approximate parametric optimization of infinite-dimensional systems

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We consider the problem of finding g ∈ Mn such that [math] where Mn is the n-dimensional subspace of the complex Hilbert space L2(0, ∞) spanned by an n-tuple of normalized eigenvectoes of the operator [math] , corresponding to eigenvalues [math] . The solution is g = Pnf and Pn denotes the orthoprojector onto Mn. From Grabowski (1991) we know that Pn can be expressed in terms of the Malmquist functions. We give an alternative approach, more convenient for application of the standard mathematical software. The problem of convergence as n → ∞ is discussed from both theoretical and numerical viewpoint. The reslts are illustrated by the problems of finding the optimal adjustment of the proportional controller stabilizing a distributed plant.

Journal Article.  0 words. 

Subjects: Mathematics

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