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We address the problem of monitoring a linear functional (c, x)Eof an unknown vectorx of a Hilbert spaceE, the available data being the observationz, in a Hilbert spaceF, of a vectorAx depending linearly onx through some known operatorAεℒ(E; F). WhenE=E
1 0), andA is injective and...
Some sharp results about Weiner and Wick products of whitenoise functionals are obtained. Using the inequality of Wick products we show to what extent scaling transformations, translations, and Sobolev differentiations can be performed on white-noise functionals.
This article considers the optimal control of the harvesting of a prey-predator system in an environment. The species are assumed to be in steady state under diffusion and Voterra-Lotka type of interaction. They are harvested for economic profit, leading to reduction of growth rates; and the...
This paper deals with approximate and exact controllability of the wave equation in finite time with interior point control acting along a curve specified in advance in the system's spatial domain. The structure of the control input is dual to the structure of the observations which describe the...
We present a new solution to the quadratic regulator problem for systems with input delays. Our approach makes use of the existing theory of the singular quadratic regulator problem for distributed systems.
In this paper we generalize the Kalman-Yakubovic lemma to infinite dimensions—or, more precisely, to semigroups of operators over a Hilbert space. The proof differs substantially from the finite-dimensional version and is based on the Paley-Wiener-Helson-Lowdenslager factorization theorem.
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