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Infinite-dimensional bilinear and stochastic balanced truncation with explicit error bounds

Published version
Peer-reviewed

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Authors

Becker, S 
Hartmann, C 

Abstract

Along the ideas of Curtain and Glover, we extend the balanced truncation method for infinite-dimensional linear systems to bilinear and stochastic systems. Specifically , we apply Hilbert space techniques used in many-body quantum mechanics to establish error bounds for the truncated system and prove convergence results. The functional analytic setting allows us to obtain mixed Hardy space error bounds for both finite-and infinite-dimensional systems, and it is then applied to the model reduction of stochastic evolution equations driven by Wiener noise.

Description

Keywords

Balanced truncation, Bilinear balanced truncation, Stochastic balanced truncation, Infinite-dimensional system theory

Journal Title

Mathematics of Control, Signals, and Systems

Conference Name

Journal ISSN

0932-4194
1435-568X

Volume Title

31

Publisher

Springer Science and Business Media LLC
Sponsorship
Engineering and Physical Sciences Research Council (EP/L016516/1)