Subspace identification – a Markov parameter approach

Estimating observability matrices or state sequences is the central component of existing subspace identification methods. In this paper a different approach, in which Markov parameters are first estimated under general input excitation, is proposed. The prominent difference of this approach is that a three-block arrangement of data matrices is used. It is shown that one advantage of this approach over other subspace algorithms is that several unbiased estimating procedures can be carried out. One immediate application is to obtain balanced or nearly balanced models directly from the estimated Markov parameters. Another application is that with the estimated Markov parameters, consistently initialized Kalman filter state sequences can be obtained, from which the system matrices can be easily determined without bias. Performance of the proposed algorithms is investigated in two case studies which are based on real data taken from two industrial systems. The algorithms developed in this paper have been implemented and are publicly available.

[1]  Nelson L. C. Chui,et al.  Criteria for informative experiments with subspace identification , 2005 .

[2]  Wallace E. Larimore,et al.  Canonical variate analysis in identification, filtering, and adaptive control , 1990, 29th IEEE Conference on Decision and Control.

[3]  J. Maciejowski,et al.  System identification using balanced parametrizations , 1997, IEEE Trans. Autom. Control..

[4]  Bart De Moor,et al.  N4SID: Subspace algorithms for the identification of combined deterministic-stochastic systems , 1994, Autom..

[5]  Patrick Dewilde,et al.  Subspace model identification Part 1. The output-error state-space model identification class of algorithms , 1992 .

[6]  Bart De Schutter,et al.  DAISY : A database for identification of systems , 1997 .

[7]  Mats Viberg,et al.  Subspace-based methods for the identification of linear time-invariant systems , 1995, Autom..

[8]  Bo Wahlberg,et al.  A linear regression approach to state-space subspace system identification , 1996, Signal Process..

[10]  Bo Wahlberg,et al.  Analysis of state space system identification methods based on instrumental variables and subspace fitting , 1997, Autom..

[11]  A. Nerode,et al.  Linear automaton transformations , 1958 .

[12]  D. Bauer.  Some asymptotic theory for the estimation of linear systems using maximum likelihood methods or subspace algorithms , 1998 .

[13]  B. Wahlberg,et al.  4SID linear regression , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[14]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[15]  Manfred Deistler,et al.  Consistency and relative efficiency of subspace methods , 1994, Autom..

[16]  James Clary,et al.  Stochastic theory of minimal realization , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[17]  Bart De Moor,et al.  A unifying theorem for three subspace system identification algorithms , 1995, Autom..

[18]  P. Faurre.  Stochastic Realization Algorithms , 1976 .

[19]  R. E. Kalman,et al.  On minimal partial realizations of a linear input/output map , 1971 .

[20]  Bart De Moor,et al.  Subspace algorithms for the stochastic identification problem, , 1993, Autom..

[21]  J. Maciejowski,et al.  System Identification Using Balanced Parameterizations , 1998 .

[22]  Manfred Deistler,et al.  Statistical analysis of novel subspace identification methods , 1996, Signal Process..

[23]  Michel Verhaegen,et al.  Identification of the deterministic part of MIMO state space models given in innovations form from input-output data , 1994, Autom..

[24]  Bo Wahlberg,et al.  On Weighting in State-Space Subspace System Identification , 1995 .

[25]  Jan M. Maciejowski,et al.  Realization of stable models with subspace methods , 1996, Autom..

[26]  Jan M. Maciejowski,et al.  An unbiased subspace algorithm with the state sequence approach. , 1998 .

[27]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .