Mathematics > Optimization and Control
[Submitted on 23 Mar 2023 (v1), last revised 6 Nov 2023 (this version, v2)]
Title:Complexity reduction of large-scale stochastic systems using linear quadratic Gaussian balancing
View PDFAbstract:In this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic systems are identified exploiting these Gramians. An associated balancing related scheme is proposed that removes unimportant information from the stochastic dynamics in order to obtain a reduced system. We show that this reduced model preserves important features like stabilizability and detectability. Additionally, a comprehensive error analysis based on eigenvalues of the Gramian pair product is conducted. This provides an a-priori criterion for the reduction quality which we illustrate in numerical experiments.
Submission history
From: Martin Redmann [view email][v1] Thu, 23 Mar 2023 17:28:27 UTC (305 KB)
[v2] Mon, 6 Nov 2023 08:37:16 UTC (319 KB)
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