Abstracts to forthcoming papers

Abstract

There already exist a fairly complete theroy for the problem of estimation and stochastic optimal control for linear distribution parameter systems, with Gaussian or non-Gaussian noise disturbance. In [8] and [12] generalizations of the familiar finite dimensional results of the kalman-bucy filter and the separtion principle are obtained using an abstract input-output Hilbert space representation for the system. However , in [8] and [12] all the input-operators are assumed to be bounded and so it does not cover the important pratical cases of control and noise on submanifolds of the spatial domain or point observations. Here we introduce unbounded system operators in the abstract iput-output Hilbert space reperesentation and thus extend all the results if [8] and [12] to allow for point observations and noise and control on submanifolds including the boundary. the theroy is illustrated by several examples