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Balanced model reduction of linear systems with nonzero initial conditions: Singular perturbation approximation

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  • Daraghmeh, Adnan
  • Hartmann, Carsten
  • Qatanani, Naji

Abstract

In this article we study balanced model reduction of linear control systems using the singular perturbation approximation. Balanced model reduction techniques have been successfully applied to systems with homogeneous initial conditions, with one of their most important features being a priori L2 and H∞ bounds for the approximation error. The main focus of this work is to derive an L2 error bound for the singular perturbation approximation for system with inhomogeneous initial conditions, extending related work on balanced truncation. This L2 error bound measures the difference between the input-output maps of the original and of the reduced initial value systems. The advantages and flexibility of this approach are demonstrated with a variety of numerical examples.

Suggested Citation

  • Daraghmeh, Adnan & Hartmann, Carsten & Qatanani, Naji, 2019. "Balanced model reduction of linear systems with nonzero initial conditions: Singular perturbation approximation," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 295-307.
    • Handle: RePEc:eee:apmaco:v:353:y:2019:i:c:p:295-307
    DOI: 10.1016/j.amc.2019.02.001
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    References listed on IDEAS

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    1. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 153-185, September.
    2. Rico Buchholz & Harald Engel & Eileen Kammann & Fredi Tröltzsch, 2013. "Erratum to: On the optimal control of the Schlögl-model," Computational Optimization and Applications, Springer, vol. 56(1), pages 187-188, September.
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    Cited by:

    1. Li, Yanpeng & Jiang, Yaolin & Yang, Ping, 2022. "Model order reduction of port-Hamiltonian systems with inhomogeneous initial conditions via approximate finite-time Gramians," Applied Mathematics and Computation, Elsevier, vol. 422(C).
    2. Becker, Simon & Hartmann, Carsten & Redmann, Martin & Richter, Lorenz, 2022. "Error bounds for model reduction of feedback-controlled linear stochastic dynamics on Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 149(C), pages 107-141.

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    More about this item

    Keywords

    Balanced truncation; Singular perturbation approximation; Error bound; Homogeneous and non-homogeneous initial conditions; L2 norm;
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    JEL classification:

    • L2 - Industrial Organization - - Firm Objectives, Organization, and Behavior

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