**Page description appears here**

“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.

     Valid XHTML 1.0 Strict

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.

PDF PDF (477 Kb)        DOI: 10.4173/mic.2009.4.2

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

[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 Hos algorithm, IEEE Trans. on Automatic Control, 1.2:153 doi:10.1109/TAC.1974.1100525

  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},
  publisher={Norwegian Society of Automatic Control}


Oct 2018: MIC reaches 3000 DOI Forward Links. The last 1000 took 2 years and 5 months.

May 2016: MIC reaches 2000 DOI Forward Links. The first 1000 took 34 years, the next 1000 took 2.5 years.

July 2015: MIC's new impact factor is now 0.778. The number of papers published in 2014 was 21 compared to 15 in 2013, which partially explains the small decrease in impact factor.

Aug 2014: For the 3rd year in a row MIC's impact factor increases. It is now 0.826.

Dec 2013: New database-driven web-design enabling extended statistics. Article number 500 is published and MIC reaches 1000 DOI Forward Links.

Jan 2012: Follow MIC on your smartphone by using the RSS feed.


July 2011: MIC passes 1000 ISI Web of Science citations.

Mar 2010: MIC is now indexed by DOAJ and has received the Sparc Seal seal for open access journals.

Dec 2009: A MIC group is created at LinkedIn and Twitter.

Oct 2009: MIC is now fully updated in ISI Web of Knowledge.