Propagator-based methods for recursive subspace model identification

The problem of the online identification of multi-input multi-output (MIMO) state-space models in the framework of discrete-time subspace methods is considered in this paper. Several algorithms, based on a recursive formulation of the MIMO Output Error State-Space (MOESP) identification class, are developed. The main goals of the proposed methods are to circumvent the huge complexity of eigenvalues or singular values decomposition techniques used by the offline algorithm and to provide consistent state-space matrices estimates in a noisy framework. The underlying principle consists in using the relationship between array signal processing and subspace identification to adjust the propagator method (originally developed in array signal processing) to track the subspace spanned by the observability matrix. The problem of the (coloured) disturbances acting on the system is solved by introducing an instrumental variable in the minimized cost functions. A particular attention is paid to the algorithmic development and to the computational cost. The benefits of these algorithms in comparison with existing methods are emphasized with a simulation study in time-invariant and time-varying scenarios.

[1]  M. Lovera.  Recursive subspace identification based on projector tracking , 2003 .

[2]  奥 宏史.  Sequential subspace state-space system identification and state estimation of unknown multivariable systems , 2000 .

[3]  B. Moor,et al.  Subspace state space system identification for industrial processes , 1998 .

[4]  Akira Ohsumi,et al.  RECURSIVE 4 SID-BASED IDENTIFICATION ALGORITHM WITH FIXED INPUT-OUTPUT DATA SIZE , 2005 .

[5]  T. Kailath,et al.  Fast identification of state-space models via exploitation of displacement structure , 1994, IEEE Trans. Autom. Control..

[6]  G. Bienvenu,et al.  Optimality of high resolution array processing using the eigensystem approach , 1983 .

[7]  David T. Westwick,et al.  Subspace identification method for ankle mechanics , 1995, Proceedings of 17th International Conference of the Engineering in Medicine and Biology Society.

[8]  M. Lovera,et al.  Recursive subspace identification based on instrumental variable unconstrained quadratic optimization , 2004 .

[9]  G. Mercère,et al.  A New Recursive Method for Subspace Identification of Noisy Systems: EIVPM , 2003 .

[10]  Arjan van der Schaft,et al.  Proceedings of the 30th IEEE Conference on Decision and Control , 1991 .

[11]  Dietmar Bauer,et al.  Asymptotic properties of subspace estimators , 2005, Autom..

[12]  Michel Verhaegen,et al.  Recursive subspace identification of linear and non-linear Wiener state-space models , 2000, Autom..

[13]  Bin Yang,et al.  Projection approximation subspace tracking , 1995, IEEE Trans. Signal Process..

[14]  Hidenori Kimura,et al.  Recursive 4SID algorithms using gradient type subspace tracking , 2002, Autom..

[15]  G. Mercère,et al.  Sequential correlation based propagator algorithm for recursive subspace identification , 2005 .

[16]  B. Friedlander.  The Overdetermined Recursive Instrumental Variable Method , 1983 .

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

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

[19]  Marco Lovera,et al.  CONVERGENCE ANALYSIS OF INSTRUMENTAL VARIABLE RECURSIVE SUBSPACE IDENTIFICATION ALGORITHMS , 2006 .

[20]  M. Abdelghani,et al.  Comparison Study of Subspace Identification Methods Applied to Flexible Structures , 1998 .

[21]  Ricardo D. Fierro,et al.  The Total Least Squares Problem: Computational Aspects and Analysis (S. Van Huffel and J. Vandewalle) , 1993, SIAM Rev..

[22]  M. Viberg,et al.  Two decades of array signal processing research: the parametric approach , 1996, IEEE Signal Process. Mag..

[23]  Richard J. Vaccaro,et al.  A Second-Order Perturbation Expansion for the SVD , 1994 .

[24]  M. Verhaegen,et al.  A fast, recursive MIMO state space model identification algorithm , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[25]  Hidenori Kimura,et al.  A RECURSIVE 4SID FROM THE INPUT‐OUTPUT POINT OF VIEW , 1999 .

[26]  V. Verdult,et al.  Filtering and System Identification: Subspace model identification , 2007 .

[27]  Tohru Katayama,et al.  Subspace Methods for System Identification , 2005 .

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

[29]  B. Friedlander,et al.  The square-root overdetermined recursive instrumental variable algorithm , 1989 .

[30]  M. Verhaegen.  Subspace model identification Part 2. Analysis of the elementary output-error state-space model identification algorithm , 1992 .

[31]  Bart De Moor,et al.  Recursive subspace identification for in flight modal analysis of airplanes , 2006 .

[32]  P. Holmes,et al.  Suppression of bursting , 1997, Autom..

[33]  T. Gustafsson.  Recursive System Identification Using Instrumental Variable Subspace Tracking , 1997 .

[34]  Thomas Kailath,et al.  ESPRIT-A subspace rotation approach to estimation of parameters of cisoids in noise , 1986, IEEE Trans. Acoust. Speech Signal Process..

[35]  M. Verhaegen,et al.  Some Experience with the MOESP Class of Subspace Model Identification Methods in Identifying the BO105 Helicopter , 1994 .

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

[37]  Michel Verhaegen,et al.  Subspace Algorithms for the Identification of Multivariable Dynamic Errors-in-Variables Models , 1997, Autom..

[38]  Jung-Lang Yu.  A novel subspace tracking using correlation-based projection approximation , 2000, Signal Process..

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

[40]  Gilles Y. Delisle,et al.  Spatial analysis using new properties of the cross-spectral matrix , 1991, IEEE Trans. Signal Process..

[41]  B. Coppotelli,et al.  Proceedings of the International Conference on Noise and Vibration Engineering , 2004 .

[42]  Tony Gustafsson,et al.  Instrumental variable subspace tracking using projection approximation , 1998, IEEE Trans. Signal Process..

[43]  Laurent Mevel,et al.  APPLICATION OF A SUBSPACE-BASED FAULT DETECTION METHOD TO INDUSTRIAL STRUCTURES , 1999 .

[44]  Gene H. Golub,et al.  Matrix computations , 1983 .

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