Partially Observed Analytic Systems with Fully Unbounded Actuators and Sensors-FEM Algorithms

Authors:
Guangcao Ji;I. Lasiecka
Affiliations:
Department of Applied Mathematics, University of Virginia, Charlottesville, VA 22903;Department of Applied Mathematics, University of Virginia, Charlottesville, VA 22903
Venue:
Computational Optimization and Applications
Year:
1998

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Abstract

Partially observed control systems described by analyticsemigroup are considered. Finite-dimensional feedback control basedon FEM approximations and accounting for incompleteobservations is constructed. It is shown that this feedback controlprovides uniform stability (in time) of the originally unstablesystem. The main novel feature of the problem is that both—controland observation operators—are modeled by fully unboundedoperators as they frequently arise in modeling of “smart” sensorsand actuators. This contributes to technical difficulties at thelevel of perturbation theory for analytic semigroups. It is shownthat a careful and rather special approximation in the area ofsupport of the unbounded control/observationoperators allows to obtain the “right” stability estimates.Theoretical results are illustrated with several examples of controlproblems governed by heat and plate equations.