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

identification, passive systems, port-hamiltonian system, 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 \&amp; 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 (2016) Stability Radii for Linear Hamiltonian Systems with Dissipation Under Structure-Preserving Perturbations. SIAM J Matrix Anal & Appl 37(4):1625–1654. https://doi.org/10.1137/16m106733 – 10.1137/16m1067330
Mehl C, Mehrmann V, Wojtylak M (2018) Linear Algebra Properties of Dissipative Hamiltonian Descriptor Systems. SIAM J Matrix Anal & Appl 39(3):1489–1519. https://doi.org/10.1137/18m116427 – 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 (1985) On the estimation of transfer functions. Automatica 21(6):677–696. https://doi.org/10.1016/0005-1098(85)90042- – 10.1016/0005-1098(85)90042-1
Peherstorfer B, Gugercin S, Willcox K (2017) Data-Driven Reduced Model Construction with Time-Domain Loewner Models. SIAM J Sci Comput 39(5):A2152–A2178. https://doi.org/10.1137/16m109475 – 10.1137/16m1094750
Astolfi A (2010) Model Reduction by Moment Matching for Linear and Nonlinear Systems. IEEE Trans Automat Contr 55(10):2321–2336. https://doi.org/10.1109/tac.2010.204604 – 10.1109/tac.2010.2046044
Benner, Computing passive reduced-order models for circuit simulation. (2004)
Daniel L, Phillips J (2002) Model order reduction for strictly passive and causal distributed systems. Proceedings of the 39th conference on Design automation - DAC ’02 4 – 10.1145/513930.513932
Freund, Reduced-order modeling of large passive linear circuits by means of the SyPVL algorithm. (1996)
Phillips JR, Daniel L, Silveira LM (2003) Guaranteed passive balancing transformations for model order reduction. IEEE Trans Comput-Aided Des Integr Circuits Syst 22(8):1027–1041. https://doi.org/10.1109/tcad.2003.81494 – 10.1109/tcad.2003.814949
Gugercin S, Polyuga RV, Beattie C, van der Schaft A (2012) Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems. Automatica 48(9):1963–1974. https://doi.org/10.1016/j.automatica.2012.05.05 – 10.1016/j.automatica.2012.05.052
Polyuga RV, van der Schaft AJ (2012) Effort- and flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems. Systems & Control Letters 61(3):412–421. https://doi.org/10.1016/j.sysconle.2011.12.00 – 10.1016/j.sysconle.2011.12.008
Wolf T, Lohmann B, Eid R, Kotyczka P (2010) Passivity and Structure Preserving Order Reduction of Linear Port-Hamiltonian Systems Using Krylov Subspaces. European Journal of Control 16(4):401–406. https://doi.org/10.3166/ejc.16.401-40 – 10.3166/ejc.16.401-406
Cherifi, (2019)
Mayo AJ, Antoulas AC (2007) A framework for the solution of the generalized realization problem. Linear Algebra and its Applications 425(2–3):634–662. https://doi.org/10.1016/j.laa.2007.03.00 – 10.1016/j.laa.2007.03.008
Willems J (1971) Least squares stationary optimal control and the algebraic Riccati equation. IEEE Trans Automat Contr 16(6):621–634. https://doi.org/10.1109/tac.1971.109983 – 10.1109/tac.1971.1099831
Willems JC (1972) Dissipative dynamical systems Part II: Linear systems with quadratic supply rates. Arch Rational Mech Anal 45(5):352–393. https://doi.org/10.1007/bf0027649 – 10.1007/bf00276494
Antoulas, (2005)
Van Der Schaft, Port-Hamiltonian systems: An introductory survey. (2006)
Beattie, (2016)
Mehrmann V, Van Dooren PM (2020) Optimal Robustness of Port-Hamiltonian Systems. SIAM J Matrix Anal Appl 41(1):134–151. https://doi.org/10.1137/19m125909 – 10.1137/19m1259092
Overton ML, Van Dooren P On computing the complex passivity radius. Proceedings of the 44th IEEE Conference on Decision and Control 7960–796 – 10.1109/cdc.2005.1583449
Hazewinkel, On invariants, canonical forms and moduli for linear, constant, finite dimensional, dynamical systems. (1976)
Youla DC, Saito M (1967) Interpolation with positive real functions. Journal of the Franklin Institute 284(2):77–108. https://doi.org/10.1016/0016-0032(67)90582- – 10.1016/0016-0032(67)90582-0
Antoulas AC (2005) A new result on passivity preserving model reduction. Systems & Control Letters 54(4):361–374. https://doi.org/10.1016/j.sysconle.2004.07.00 – 10.1016/j.sysconle.2004.07.007
Dirksz DA, Scherpen JMA, van der Schaft AJ, Steinbuch M (2015) Notch Filters for Port-Hamiltonian Systems. IEEE Trans Automat Contr 60(9):2440–2445. https://doi.org/10.1109/tac.2015.239055 – 10.1109/tac.2015.2390552
Gugercin S, Antoulas AC (2003) A survey of balancing methods for model reduction. 2003 European Control Conference (ECC) 968–97 – 10.23919/ecc.2003.7085084
Duff, (2019)