“A Bootstrap Subspace Identification Method: Comparing Methods for Closed Loop Subspace Identification by Monte Carlo Simulations”

Authors: David Di Ruscio,
Affiliation: Telemark University College
Reference: 2009, Vol 30, No 4, pp. 203-222.

Keywords: Subspace, Identification, Closed loop, Linear Systems, Kalman filter, Modeling

Abstract: A novel promising bootstrap subspace system identification algorithm for both open and closed loop systems is presented. An outline of the SSARX algorithm by Jansson (2003) is given and a modified SSARX algorithm is presented. Some methods which are consistent for closed loop subspace system identification presented in the literature are discussed and compared to a recently published subspace algorithm which works for both open as well as for closed loop data, i.e., the DSR_e algorithm as well as the new bootstrap subspace method presented in this paper. Experimental comparisons are performed by Monte Carlo simulations.

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DOI forward links to this article:
[1] Jan-Willem van Wingerden, Marco Lovera, Marco Bergamasco, Michel Verhaegen and Gijs van der Veen (2013), doi:10.1049/iet-cta.2012.0653
[2] Masoud Kheradmandi and Prashant Mhaskar (2018), doi:10.1016/j.compchemeng.2017.11.016
[3] Hiroshi Oku (2014), doi:10.5687/sss.2014.155
[4] Christer Dalen and David Di Ruscio (2019), doi:10.4173/mic.2019.4.2
References:
[1] Chiuso, A. (2007). On the relation between CCA and predictor based subspace identification, IEEE Transaction on Automatic Control, 5.10:1795--1812 doi:10.1109/TAC.2007.906159
[2] Chiuso, A. (2007). The role of vector autoregressive modeling in predictor-based subspace identification, Automatica, 4.6:1034--1048 doi:10.1016/j.automatica.2006.12.009
[3] Chiuso, A. Picci, G. (2005). Consistency analysis of some closed-loop subspace identification methods, Automatica, 4.3:377--391 doi:10.1016/j.automatica.2004.10.015
[4] Di Ruscio, D. (1996). Combined Deterministic and Stochastic System Identification and Realization: DSR-a subspace approach based on observations, Modeling, Identification and Control, 1.3:193--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.
[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. 2.3:125--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.
[9] Di Ruscio, D. (2009). Closed and Open Loop Subspace System Identification of the Kalman Filter, Modeling, Identification and Control, 3.2:71--86 doi:10.4173/mic.2009.2.3
[10] Ho, B.L. Kalman, R.E. (1966). Effective construction of linear state-variable models from input/output functions, Regelungstechnik, 1.12:545--592.
[11] Jansson, M. (2003). Subspace Identification and ARX Modeling, In 13th IFAC Symp. on System Identif.
[12] Jansson, M. (2005). A new subspace identification method for open and closed loop data, In IFAC World Congress.
[13] Larimore, W.E. (1983). System identification, reduced order filtering and modeling via canonical variate analysis, In Proc. Am. Control Conf. pp. 445--451.
[14] Larimore, W.E. (1990). Canonical variate analysis in identification, filtering and adaptive control, In Proc. 29th Conf. on Decision and Control. pp. 596--604.
[15] Ljung, L. (1999). System Identification: Theory for the User, Prentice Hall PTR.
[16] Ljung, L. McKelvey, T. (1995). Subspace identification from closed loop data, Technical Report LiTH-ISY-R-1752, Linkoping University, Sweden.
[17] Ljung, L. McKelvey, T. (1996). Subspace identification from closed loop data, Signal Processing, 52(12):209--215 doi:10.1016/0165-1684(96)00054-0
[18] Overschee, P.V. deMoor, B. (1996). Subspace identification for linear systems, Kluwer Acad. Publ.
[19] Qin, S.J. Ljung, L. (2003). Closed-loop subspace identification with innovation estimation, In Proc. 13th IFAC SYSID Symposium. pp. 887--892.
[20] Qin, S.J. Ljung, L. (2006). On the role of future horizon in closed-loop subspace identification, In Proc. 14th IFAC SYSID Symposium. pp. 1080--1084.
[21] Qin, S.J., Weilu, L., Ljung, L. (2005). A novel subspace identification approach with enforced causal models, Automatica, 4.12:2043--2053 doi:10.1016/j.automatica.2005.06.010
[22] Zeiger, H. McEwen, A. (1974). Approximate linear realizations of given dimensions via Ho´s algorithm, IEEE Trans. on Automatic Control, 1.2:153 doi:10.1109/TAC.1974.1100525


BibTeX:
@article{MIC-2009-4-2,
  title={{A Bootstrap Subspace Identification Method: Comparing Methods for Closed Loop Subspace Identification by Monte Carlo Simulations}},
  author={Di Ruscio, David},
  journal={Modeling, Identification and Control},
  volume={30},
  number={4},
  pages={203--222},
  year={2009},
  doi={10.4173/mic.2009.4.2},
  publisher={Norwegian Society of Automatic Control}
};