From Data to Reduced-Order Models via Generalized Balanced Truncation

• 成果类型: Article
• 署名作者: Burohman, Azka Muji; Besselink, Bart; Scherpen, Jacquelien M. A.; Camlibel, M. Kanat
• 署名单位: University of Groningen; University of Groningen; University of Groningen
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3238856
• 发表日期: 2023
• 页码: 6160-6175
• 关键词: Data-driven model reduction; Data informativity; error bounds; generalized balancing

摘要

This article proposes a data-driven model reduction approach on the basis of noisy data with a known noise model. Firstl, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin projection to all systems explaining the data characterized in a large-dimensional quadratic matrix inequality (QMI) can again be characterized in a lower-dimensional QMI. Next, we develop a data-driven generalized balanced truncation method that relies on two steps. First, we provide necessary and sufficient conditions such that systems explaining the data have common generalized Gramians. Second, these common generalized Gramians are used to construct matrices that allow to characterize a class of reduced-order models via generalized balanced truncation in terms of a lower-dimensional QMI by applying the data reduction concept. Additionally, we present alternative procedures to compute a priori and a posteriori upper bounds with respect to the true system generating the data. Finally, the proposed techniques are illustrated by means of application to an example of a system of a cart with a double-pendulum.