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IMA Journal of Mathematical Control and Information 1999 16(2):115-123; doi:10.1093/imamci/16.2.115
© 1999 by Institute of Mathematics and its Applications
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Approximate parametric optimization of infinite-dimensional systems

PIOTR GRABOWSKI {dagger}

Institute of Automatics, Academy of Mining and Metallurgy, al. Mickiewicza 30, Bl, rm.314, PL-30-059 Cracow, Poland

We consider the problem of finding g Mn such that

where Mn is the n-dimensional subspace of the complex Hilbert space L2(0, {infty}) spanned by an n-tuple of normalized eigenvectoes of the operator

, corresponding to eigenvalues . 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 -> {infty} 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.

{dagger} Email: pgrab{at}ia.agh.edu.pl


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