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Titel
Interpolation-based ℋ₂-model reduction of bilinear control systems / Peter Benner, Tobias Breiten
VerfasserBenner, Peter ; Breiten, Tobias
KörperschaftMax-Planck-Institut für Dynamik Komplexer Technischer Systeme
ErschienenMagdeburg : Max Planck Institute for Dynamics of Complex Technical Systems, July 12, 2011
Umfang1 Online-Ressource (29 Seiten = 0,5 MB) : Diagramme
SpracheEnglisch
SerieMax Planck Institute Magdeburg Preprints ; 11-02
URNurn:nbn:de:gbv:3:2-63798 
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Interpolation-based ℋ₂-model reduction of bilinear control systems [0.5 mb]
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Abstract: In this paper, we will discuss the problem of optimal model order reduction of bilinear control systems with respect to the generalization of the well-known ℋ2-norm for linear systems. We revisit existing first order necessary conditions for ℋ2-optimality based on the solutions of generalized Lyapunov equations arising in bilinear system theory and present an iterative algorithm which, upon convergence, will yield a reduced system fulfilling these conditions. While this approach relies on the solution of certain generalized Sylvester equations, we will establish a connection to another method based on generalized rational interpolation. This will lead to another way of computing the ℋ2-norm of a bilinear system and will extend the pole-residue optimality conditions for linear systems, also allowing for an adaption of the successful iterative rational Krylov algorithm (IRKA) to bilinear systems. By means of several numerical examples, we will then demonstrate that the new techniques outperform the method of balanced truncation for bilinear systems with regard to the relative ℋ2-error.

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Abstract: In this paper we will discuss the problem of optimal model order reduction of bilinear control systems with respect to the generalization of the well-known ℋ2-norm for linear systems. We revisit existing first order necessary conditions for ℋ2-optimality based on the solutions of generalized Lyapunov equations arising in bilinear system theory and present an iterative algorithm which upon convergence will yield a reduced system fulfilling these conditions. While this approach relies on the solution of certain generalized Sylvester equations we will establish a connection to another method based on generalized rational interpolation. This will lead to another way of computing the ℋ2-norm of a bilinear system and will extend the pole-residue optimality conditions for linear systems also allowing for an adaption of the successful iterative rational Krylov algorithm (IRKA) to bilinear systems. By means of several numerical examples we will then demonstrate that the new techniques outperform the method of balanced truncation for bilinear systems with regard to the relative ℋ2-error.