PARTIALLY OBSERVED ANALYTIC SYSTEMS WITH FULLY UNBOUNDED ACTUATORS AND SENSORS FEM ALGORITHMS

Partially observed control systems described by analytic semigroup are considered. Finite-dimensional feedback control based on FEM approxim ations and accounting for incomplete observations is constructed. It i s shown that this feedback control provides uniform stability (in time ) of the originally unstable system. The main novel feature of the pro blem is that both-control and observation operators-are modeled by ful ly unbounded operators as they frequently arise in modeling of ''smart '' sensors and actuators. This contributes to technical difficulties a t the level of perturbation theory for analytic semigroups. It is show n that a careful and rather special approximation in the area of suppo rt of the unbounded control/observation operators allows to obtain the ''right'' stability estimates. Theoretical results are illustrated wi th several examples of control problems governed by heat and plate equ ations.