Identification of port-Hamiltonian systems from frequency response data

Authors

Peter Benner, Pawan Goyal, Paul Van Dooren

Abstract

In this paper, we study the identification problem of strictly passive systems from frequency response data. We present a simple construction approach based on the Mayo–Antoulas generalized realization theory that automatically yields a port-Hamiltonian realization for every strictly passive system with simple spectral zeros. Furthermore, we discuss the construction of a frequency-limited port-Hamiltonian realization. We illustrate the proposed method by means of several examples.

Keywords

Passive systems; Port-Hamiltonian system; Identification; Tangential interpolation

Citation

• Journal: Systems & Control Letters
• Year: 2020
• Volume: 143
• Issue:
• Pages: 104741
• Publisher: Elsevier BV
• DOI: 10.1016/j.sysconle.2020.104741

BibTeX

@article{Benner_2020,
  title={{Identification of port-Hamiltonian systems from frequency response data}},
  volume={143},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2020.104741},
  journal={Systems & Control Letters},
  publisher={Elsevier BV},
  author={Benner, Peter and Goyal, Pawan and Van Dooren, Paul},
  year={2020},
  pages={104741}
}

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References

• Mehl, C., Mehrmann, V. & Sharma, P. Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations. SIAM Journal on Matrix Analysis and Applications vol. 37 1625–1654 (2016) – 10.1137/16m1067330
• Mehl, C., Mehrmann, V. & Wojtylak, M. Linear Algebra Properties of Dissipative Hamiltonian Descriptor Systems. SIAM Journal on Matrix Analysis and Applications vol. 39 1489–1519 (2018) – 10.1137/18m1164275
• Bond, Parameterized model order reduction of nonlinear dynamical systems. (2005)
• Bond, Guaranteed stable projection-based model reduction for indefinite and unstable linear systems. (2008)
• Lennart, (1999)
• van Overschee, (2012)
• Verhaegen, (2007)
• Gonzalez, (1996)
• Ohayon, (1997)
• Ljung, L. On the estimation of transfer functions. Automatica vol. 21 677–696 (1985) – 10.1016/0005-1098(85)90042-1
• Peherstorfer, B., Gugercin, S. & Willcox, K. Data-Driven Reduced Model Construction with Time-Domain Loewner Models. SIAM Journal on Scientific Computing vol. 39 A2152–A2178 (2017) – 10.1137/16m1094750
• Astolfi, A. Model Reduction by Moment Matching for Linear and Nonlinear Systems. IEEE Transactions on Automatic Control vol. 55 2321–2336 (2010) – 10.1109/tac.2010.2046044
• Benner, Computing passive reduced-order models for circuit simulation. (2004)
• Daniel, L. & Phillips, J. Model order reduction for strictly passive and causal distributed systems. Proceedings of the 39th conference on Design automation - DAC ’02 46 (2002) doi:10.1145/513918.513932 – 10.1145/513918.513932
• Freund, Reduced-order modeling of large passive linear circuits by means of the SyPVL algorithm. (1996)
• Phillips, J. R., Daniel, L. & Silveira, L. M. Guaranteed passive balancing transformations for model order reduction. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems vol. 22 1027–1041 (2003) – 10.1109/tcad.2003.814949
• Gugercin, S., Polyuga, R. V., Beattie, C. & van der Schaft, A. Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems. Automatica vol. 48 1963–1974 (2012) – 10.1016/j.automatica.2012.05.052
• Polyuga, R. V. & van der Schaft, A. J. Effort- and flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems. Systems & Control Letters vol. 61 412–421 (2012) – 10.1016/j.sysconle.2011.12.008
• Wolf, T., Lohmann, B., Eid, R. & Kotyczka, P. Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces. European Journal of Control vol. 16 401–406 (2010) – 10.3166/ejc.16.401-406
• Cherifi, (2019)
• Mayo, A. J. & Antoulas, A. C. A framework for the solution of the generalized realization problem. Linear Algebra and its Applications vol. 425 634–662 (2007) – 10.1016/j.laa.2007.03.008
• Willems, J. Least squares stationary optimal control and the algebraic Riccati equation. IEEE Transactions on Automatic Control vol. 16 621–634 (1971) – 10.1109/tac.1971.1099831
• Willems, J. C. Dissipative dynamical systems Part II: Linear systems with quadratic supply rates. Archive for Rational Mechanics and Analysis vol. 45 352–393 (1972) – 10.1007/bf00276494
• Antoulas, (2005)
• Van Der Schaft, Port-Hamiltonian systems: An introductory survey. (2006)
• Beattie, (2016)
• Mehrmann, V. & Van Dooren, P. M. Optimal Robustness of Port-Hamiltonian Systems. SIAM Journal on Matrix Analysis and Applications vol. 41 134–151 (2020) – 10.1137/19m1259092
• Hazewinkel, On invariants, canonical forms and moduli for linear, constant, finite dimensional, dynamical systems. (1976)
• Youla, D. C. & Saito, M. Interpolation with positive real functions. Journal of the Franklin Institute vol. 284 77–108 (1967) – 10.1016/0016-0032(67)90582-0
• Antoulas, A. C. A new result on passivity preserving model reduction. Systems & Control Letters vol. 54 361–374 (2005) – 10.1016/j.sysconle.2004.07.007
• Dirksz, D. A., Scherpen, J. M. A., van der Schaft, A. J. & Steinbuch, M. Notch Filters for Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 60 2440–2445 (2015) – 10.1109/tac.2015.2390552
• Gugercin, S. & Antoulas, A. C. A survey of balancing methods for model reduction. 2003 European Control Conference (ECC) 968–973 (2003) doi:10.23919/ecc.2003.7085084 – 10.23919/ecc.2003.7085084
• Duff, (2019)