Approximate parametric optimization of infinite-dimensional systems

We consider the problem of finding g M_n such that where M_n is the n-dimensional subspace of the complexHilbert space L²(0, ) spanned by an n-tuple of normalized eigenvectoesof the operator , corresponding to eigenvalues. The solution is g = P_nf and P_n denotesthe orthoprojector onto M_n. From Grabowski (1991) we know thatP_n can be expressed in terms of the Malmquist functions. Wegive an alternative approach, more convenient for applicationof the standard mathematical software. The problem of convergenceas n is discussed from both theoretical and numerical viewpoint.The reslts are illustrated by the problems of finding the optimaladjustment of the proportional controller stabilizing a distributedplant. Email: pgrab{at}ia.agh.edu.pl