Structural identifiability of linear Port Hamiltonian systems

Authors

Silviu Medianu, Laurent Lefèvre

Abstract

This paper, puts in discussion the structural identifiability of LTI Port-Controlled Hamiltonian (PCH) systems, in order to develop a specific identification and control theory. This is due to their remarkable properties of power conservation and stability under power preserving interconnection. The main part of the paper, presents a power based identifiability approach, with specific propositions and definitions. It is based on the power knowledge associated with the system ports, interconnected by a Dirac structure, for selected input signals. In a preliminary section, corresponding transfer functions, system outputs, Markov parameters, observability conditions, port-observability or infinite Grammians are defined for each port. Beside this, a port-identifiability concept is introduced for the identifiability analysis of one port. It is proved that between the input and system ports, a specific model can be determined for identification analysis, preserving in the same time the PCH structure. As examples to demonstrate the theory, a controlled LC circuit and a DC motor are selected for the lossless and lossy cases, respectively.

Keywords

Port Hamiltonian systems; LTI systems; Structural identifiability; Port-observability; Global–local identifiability; Port-identifiability

Citation

• Journal: Systems & Control Letters
• Year: 2021
• Volume: 151
• Issue:
• Pages: 104915
• Publisher: Elsevier BV
• DOI: 10.1016/j.sysconle.2021.104915

BibTeX

@article{Medianu_2021,
  title={{Structural identifiability of linear Port Hamiltonian systems}},
  volume={151},
  ISSN={0167-6911},
  DOI={10.1016/j.sysconle.2021.104915},
  journal={Systems & Control Letters},
  publisher={Elsevier BV},
  author={Medianu, Silviu and Lefèvre, Laurent},
  year={2021},
  pages={104915}
}

Download the bib file

References

• Miao, H., Xia, X., Perelson, A. S. & Wu, H. On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics. SIAM Review vol. 53 3–39 (2011) – 10.1137/090757009
• van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
• Bellman, R. & Åström, K. J. On structural identifiability. Mathematical Biosciences vol. 7 329–339 (1970) – 10.1016/0025-5564(70)90132-x
• Cantó, B., Coll, C. & Sánchez, E. Identifiability for a Class of Discretized Linear Partial Differential Algebraic Equations. Mathematical Problems in Engineering vol. 2011 (2011) – 10.1155/2011/510519
• Dochain, D. Structural identifiability of biokinetic models of activated sludge respiration. Water Research vol. 29 2571–2578 (1995) – 10.1016/0043-1354(95)00106-u
• Glad, Structural identifiability: tools and applications. (1999)
• Karlsson, J., Anguelova, M. & Jirstrand, M. An Efficient Method for Structural Identifiability Analysis of Large Dynamic Systems*. IFAC Proceedings Volumes vol. 45 941–946 (2012) – 10.3182/20120711-3-be-2027.00381
• Raue, A. et al. Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics vol. 25 1923–1929 (2009) – 10.1093/bioinformatics/btp358
• Yates, J. W., Jones, R. O., Walker, M. & Cheung, S. A. Structural identifiability and indistinguishability of compartmental models. Expert Opinion on Drug Metabolism & Toxicology vol. 5 295–302 (2009) – 10.1517/17425250902773426
• Zhang, A general linear non-Gaussian state-space model: identifiability, identification and applications. (2011)
• Bley, (1983)
• Jacquez, (1972)
• Pohjanpalo, H. System identifiability based on the power series expansion of the solution. Mathematical Biosciences vol. 41 21–33 (1978) – 10.1016/0025-5564(78)90063-9
• Anderson, (2013)
• Walter, E. & Lecourtier, Y. Unidentifiable compartmental models: what to do? Mathematical Biosciences vol. 56 1–25 (1981) – 10.1016/0025-5564(81)90025-0
• Ljung, L. & Glad, T. On global identifiability for arbitrary model parametrizations. Automatica vol. 30 265–276 (1994) – 10.1016/0005-1098(94)90029-9
• Denis-Vidal, L. & Joly-Blanchard, G. An easy to check criterion for (un)indentifiability of uncontrolled systems and its applications. IEEE Transactions on Automatic Control vol. 45 768–771 (2000) – 10.1109/9.847119
• Walter, Guaranteed numerical computation as an alternative to computer algebra for testing models for identifiability. (2004)
• Chantre, Physical modeling and parameter identification of a heat exchanger. (1994)
• Medianu, Identifiability of linear lossless port controlled hamiltonian systems. (2013)
• Lupu, Structural identifiability of linear lossy port controlled hamiltonian systems. (2016)
• Maschke, B. M. & van der Schaft, A. J. Port-Controlled Hamiltonian Systems: Modelling Origins and Systemtheoretic Properties. IFAC Proceedings Volumes vol. 25 359–365 (1992) – 10.1016/s1474-6670(17)52308-3
• Antoulas, (2005)
• Ljung, (1999)