“Combined Deterministic and Stochastic System Identification and Realization: DSR - A Subspace Approach Based on Observations”

Authors: David Di Ruscio,
Affiliation: Telemark University College
Reference: 1996, Vol 17, No 3, pp. 193-230.

Keywords: System identification, subspace methods, stochastic and deterministic systems, state-space methods, time series analysis

Abstract: A numerically stable and general algorithm for identification and realization of a complete dynamic linear state space model, including the system order, for combined deterministic and stochastic systems from time series is presented. A special property of this algorithm is that the innovations covariance matrix and the Markov parameters for the stochastic sub-system are determined directly from a projection of known data matrices, without e.g. recursions of non-linear matrix Riccatti equations. A realization of the Kalman filter gain matrix is determined from the estimated extended observability matrix and the Markov parameters. Monte Carlo simulations are used to analyze the statistical properties of the algorithm as well as comparing with existing algorithms.

PDF PDF (4546 Kb)        DOI: 10.4173/mic.1996.3.3

DOI forward links to this article:
[1] A. Sæther, C. Arakaki, C. Ratnayake and D. Di Ruscio (2009), doi:10.1080/02726350902991007
[2] S. Joe Qin, Weilu Lin and Lennart Ljung (2005), doi:10.1016/j.automatica.2005.06.010
[3] Dionisio Bernal (2013), doi:10.1016/j.ymssp.2013.02.012
[4] David Di Ruscio (2003), doi:10.4173/mic.2003.3.1
[5] Dionisio Bernal (2011), doi:10.1002/stc.383
[6] Bernt Lie, David Di Ruscio, Rolf Ergon, Bjørn Glemmestad, Maths Halstensen, Finn Haugen, Saba Mylvaganam, Nils-Olav Skeie and Dietmar Winkler (2009), doi:10.4173/mic.2009.3.4
[7] Rolf Ergon (1998), doi:10.4173/mic.1998.2.2
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[10] Jin Wang and S.Joe Qin (2002), doi:10.1016/S0959-1524(02)00016-1
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[13] David Di Ruscio (2009), doi:10.4173/mic.2009.2.3
[14] David Di Ruscio (2013), doi:10.4173/mic.2013.3.2
[15] Dionisio Bernal (2004), doi:10.1061/(ASCE)0733-9399(2004)130:9(1083)
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[46] Dalton Fellipe Casamali, Antonio Felipe da Cunha de Aquino and Aguinaldo Silveira e Silva (2023), doi:10.1007/s40313-023-01034-0
References:
[1] DI RUSCIO, D. (1994). Methods for the identification of state space models from input and output measurements, SYSID 94, The 10th IFAC Symposium on System Identification, Copenhagen, July 4-6.
[2] DI RUSCIO, D. (1995). A method for the identification of state space models from input and output measurements, Modeling, Identification and Control, vol. 16, no. 3. Program commercial available by Fantoft Process AS, Box 306, N-1301 Sandvika.
[3] DI RUSCIO. D. (1995). A method for identification of combined deterministic and stochastic systems, Proceedings of the third European Control Conference, ECC95, Roma, September 5-8, pp. 429-434.
[4] DI RUSCIO, D., HOLMBERG, A. (1996). Subspace identification for dynamic process analysis and modeling, Control Systems 96, Halifax, Nova Scotia, May 1996.
[5] GOLUB, G.H., VAN LOAN, C.F. (1983). Matrix Computations, North Oxford Academic Publishers Ltd.
[6] LARIMORE, W.E. (1983). System identification, reduced order filtering and modeling via canonical variate analysis, Proc. of the American Control Conference, San Francisco, USA, pp. 445-451.
[7] LARIM0RE, W.E. (1990). Canonical Variate Analysis in Identification, Filtering and Adaptive Control, Proc. of the 29th Conference on Decision and Control, Honolulu, Hawaii, December 1990, pp. 596-604.
[8] LJUNG, L. (1991). System Identification Toolbox, The Mathworks, Inc.
[9] FAURRE, P.L. (1976). Stochastic realization algorithms, In R.K. Mehra and D.G. Lainiotis (eds), System Identification: Advances and Case Studies, Academic Press doi:10.1016/S0076-5392(08)60868-1
[10] KALMAN, R.E., FALB, P.L., ARBIB, M.A. (1969). Topics in mathematical system theory, McGraw-Hill Book Company.
[11] KUNG, S.Y. (1978). A new identification and Model Reduction Algorithm via Singular Value Decomposition, Conf on Circuits, Systems and Computers, Pacific Grove, CA, November 1978, pp. 705-714.
[12] MOORE., B.C. (1981). Principal Component Analysis in Linear Systems: Controllability, Observability, and Model Reduction, IEEE Trans. on Automatic Control, Vol. AC-26, pp. 17-31.
[13] VAN OVERSCHEE, P., DE MOOR, B. (1994). N4SID: Subspace Algorithms for the Identification of Combined Deterministic Stochastic Systems, Automatica, vol. 30, no. 1, pp. 75-94 doi:10.1016/0005-1098(94)90230-5
[14] VAN OVERSCHEE, P. (1995). Subspace Identification: theory-implementation-application, PhD thesis, Katholieke Universiteit Leuven, Belgium.
[15] VAN OVERSCHEE, P., DE MOOR, B. (1996). A Unifying Theorem for Three Subspace System Identification Algorithms, Automatica, vol. 31, no. 12, pp. 1853-1864 doi:10.1016/0005-1098(95)00072-0
[16] VERHAGEN, M. (1994). Identification of the deterministic part of MIMO state space models given on innovations form from input output data, Automatica, vol. 30, no. 1, pp. 61-74 doi:10.1016/0005-1098(94)90229-1
[17] VIBERG, M. (1995). Subspace-Based Methods for the Identification of Linear Time-invariant Systems, Automatica, vol. 31, no. 12, pp. 1835-1851 doi:10.1016/0005-1098(95)00107-5


BibTeX:
@article{MIC-1996-3-3,
  title={{Combined Deterministic and Stochastic System Identification and Realization: DSR - A Subspace Approach Based on Observations}},
  author={Di Ruscio, David},
  journal={Modeling, Identification and Control},
  volume={17},
  number={3},
  pages={193--230},
  year={1996},
  doi={10.4173/mic.1996.3.3},
  publisher={Norwegian Society of Automatic Control}
};