Finite-dimensional controller design for semilinear parabolic systems |
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Authors: | Y. Yan D. Coca V. Barbu |
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Affiliation: | aDepartment of Automatic Control & Systems Engineering, The University of Sheffield, Mappin Street, Sheffield, S1 3JD, UK;bDepartment of Mathematics, Alexandru Ioan Cuza University of Iasi, Bulevardul Carol I, Nr. 11, 700506, Iasi, Romania |
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Abstract: | This paper considers the stabilization of steady-state solutions of a semilinear parabolic system using finite-dimensional feedback controllers with support in an arbitrary open subset and which are active in one equation only. It is shown that such a controller, with dimension given by the largest algebraic multiplicity of the unstable eigenvalues of the linearized system, exponentially stabilizes the steady-state solution. An optimal design methodology for these types of controllers, which is based on the finite element approximation of the semilinear parabolic system, is introduced and illustrated by numerical simulation examples. |
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Keywords: | Parabolic system Feedback controller Riccati equation Finite element method |
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