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Balanced Truncation Model Reduction for Lifted Nonlinear Systems

In: Realization and Model Reduction of Dynamical Systems

Author

Listed:
  • 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)

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.

Suggested Citation

  • Boris Kramer & Karen Willcox, 2022. "Balanced Truncation Model Reduction for Lifted Nonlinear Systems," Springer Books, in: Christopher Beattie & Peter Benner & Mark Embree & Serkan Gugercin & Sanda Lefteriu (ed.), Realization and Model Reduction of Dynamical Systems, pages 157-174, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-95157-3_9
    DOI: 10.1007/978-3-030-95157-3_9
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