“On subspace system identification methods”

Authors: David Di Ruscio and Christer Dalen,
Affiliation: University of South-Eastern Norway
Reference: 2022, Vol 43, No 4, pp. 119-130.

Keywords: System identification, subspace methods, stochastic systems, monte carlo

Abstract: An open and closed loop subspace system identification algorithm DSRe is compared to competitive open loop algorithms, DSR, and N4SID. Additionally, DSRe is compared vs the optimal Prediction Error Method (PEM). Monte Carlo simulations with discrete random state space models are used for testing the subspace identification algorithms in the numerical simulation section.

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References:
[1] DiRuscio, D. (1994). Methods for the identification of state space models from input and output measurements, 1994. The 10 IFAC symposium on system identification SYSID’94, Copenhagen, 4-6 July.
[2] Di Ruscio, D. (1994). Methods for the identification of state space models from input and output measurements, In 10th IFAC Symp. on System Identif. 1994.
[3] DiRuscio, D. (1995). A method for the identification of state space models from input and output measurements, Modeling, Identification and Control. 16(3):129--143. doi:10.4173/mic.1995.3.2
[4] Di Ruscio, D. (1996). Combined Deterministic and Stochastic System Identification and Realization: DSR-a subspace approach based on observations, Modeling, Identification and Control. 17(3):193--230. doi:10.4173/mic.1996.3.3
[5] Di Ruscio, D. (1997). On subspace identification of the extended observability matrix, In 36th Conf. on Decision and Control. 1997.
[6] Di Ruscio, D. (2000). A weighted view of the partial least squares algorithm, Automatica. 36(6):831--850. doi:10.1016/S0005-1098(99)00210-1
[7] Di Ruscio, D. (2003). Subspace System Identification of the Kalman Filter, Modeling, Identification and Control. 24(3):125--157. doi:10.4173/mic.2003.3.1
[8] Di Ruscio, D. (2008). Subspace system identification of the Kalman filter: open and closed loop systems, In Proc. Intl. Multi-Conf. on Engineering and Technological Innovation. 2008.
[9] DiRuscio, D. (2009). A Bootstrap Subspace Identification Method: Comparing Methods for Closed Loop Subspace Identification by Monte Carlo Simulations, Modeling, Identification and Control, 2009. 30(4):203--222. doi:10.4173/mic.2009.4.2
[10] DiRuscio, D. (2009). Closed and Open Loop Subspace System Identification of the Kalman Filter, Modeling, Identification and Control, 2009. 30(2):71--86. doi:10.4173/mic.2009.2.3
[11] Hestenes, M.R. and Stiefel, E. (1952). Methods for Conjugate gradients for Solving Linear Systems, J. Res. National Bureau of Standards. 49(6):409--436.
[12] Ho, B.L. and Kalman, R.E. (1966). Effective construction of linear state-variable models from input/output functions, Regelungstechnik. 14(12):545--592.
[13] Ljung, L. (1999). System Identification: Theory for the User, Prentice Hall information and system sciences series. Prentice Hall PTR.
[14] Ljung, L. (2013). Some classical and some new ideas for identification of linear systems, Journal of Control, Automation and Electrical Systems. 24. doi:10.1007/s40313-013-0004-7
[15] MATLAB. (2020). version 9, 9.0.1718557 (R2020b). The MathWorks Inc., Natick, Massachusetts, USA. Control System Toolbox, Version 10.9. System Identification Toolbox, Version 9.13.
[16] Nilsen, G.W. (2005). Topics in open and closed loop subspace system identification: finite data based methods, Ph.D. thesis, NTNU-HiT. ISBN 82-471-7357-3.
[17] Overschee, P.V. and deMoor, B. (1994). N4SID: Subspace Algorithms for the Identification of Combined Deterministic Stochastic Systems, Automatica. 30(1):75--93. doi:10.1016/0005-1098(94)90230-5
[18] Overschee, P.V. and deMoor, B. (1996). Subspace identification for linear systems, Kluwer Acad. Publ.
[19] Qin, S., Lin, W., and Ljung, L. (2005). A novel subspace identification approach with enforced causal models, Automatica. 41(12):2043--2053. doi:10.1016/j.automatica.2005.06.010
[20] Tuomo Salonen / SIM Finnish Aviation Museum. (2017). Saab gripen at the kaivopuisto air show in june, 2017. https://en.wikipedia.org/wiki/Saab_JAS_39_Gripen#/media/File:Saab_JAS_39_Gripen_at_Kaivopuisto_Air_Show,_June_2017_(altered)_copy.jpg. Online; accesed 08-0.5-22. The original picture has been edited.
[21] vander Veen, G., van Wingerden, J.-W., Bergamasco, M., Lovera, M., and Verhaegen, M. (2013). Closed-loop subspace identification methods: an overview, IET Control Theory & Applications. 7(10):1339--1358. doi:10.1049/iet-cta.2012.0653
[22] Wang, J. and Qin, S.J. (2002). A new subspace identification approach based on principal component analysis, Journal of Process Control. 12:841--855.
[23] Zeiger, H. and McEwen, A. (1974). Approximate linear realizations of given dimensions via Ho's algorithm, IEEE Trans. on Automatic Control. 19(2):153. doi:10.1109/TAC.1974.1100525


BibTeX:
@article{MIC-2022-4-1,
  title={{On subspace system identification methods}},
  author={Di Ruscio, David and Dalen, Christer},
  journal={Modeling, Identification and Control},
  volume={43},
  number={4},
  pages={119--130},
  year={2022},
  doi={10.4173/mic.2022.4.1},
  publisher={Norwegian Society of Automatic Control}
};