Balanced Truncation Model Reduction for Lifted Nonlinear Systems

Boris Kramer () and Karen Willcox ()
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Boris Kramer: University of California San Diego, Department of Mechanical and Aerospace Engineering
Karen Willcox: University of Texas at Austin, Oden Institute for Computational Engineering Science

A chapter in Realization and Model Reduction of Dynamical Systems, 2022, pp 157-174 from Springer

Abstract: Abstract We present a balanced truncation model reduction approach for a class of nonlinear systems with time-varying and uncertain inputs. First, our approach brings the nonlinear system into quadratic-bilinear (QB) form via a process called lifting, which introduces transformations via auxiliary variables to achieve the specified model form. Second, we extend a recently developed QB balanced truncation method to be applicable to such lifted QB systems that share the common feature of having a system matrix with zero eigenvalues. We illustrate this framework and the multi-stage lifting transformation on a tubular reactor model. In the numerical results we show that our proposed approach can obtain reduced-order models that are more accurate than proper orthogonal decomposition reduced-order models in situations where the latter are sensitive to the choice of training data.

Keywords: Balanced truncation; Nonlinear model reduction; Lifting transformation; Quadratic-bilinear models (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-95157-3_9

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DOI: 10.1007/978-3-030-95157-3_9

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