Subspace-based methods for the identification of linear time-invariant systems

Subspace-based methods for system identification have attracted much attention during the past few years. This interest is due to the ability of providing accurate state-space models for multivariable linear systems directly from input-output data. The methods have their origin in classical state-space realization theory as developed in the 1960s. The main computational tools are the QR and the singular-value decompositions. Here, an overview of existing subspace-based techniques for system identification is given. The methods are grouped into the classes of realization-based and direct techniques. Similarities between different algorithms are pointed out, and their applicability is commented upon. We also discuss some recent ideas for improving and extending the methods. A simulation example is included for comparing different algorithms. The subspace-based approach is found to perform competitive with respect to prediction-error methods, provided the system is properly excited.

[1]  Jan C. Willems,et al.  From time series to linear system - Part I. Finite dimensional linear time invariant systems , 1986, Autom..

[2]  Robert E. Skelton,et al.  Modeling Hubble Space Telescope Flight Data by Q-Markov Cover Identification , 1992 .

[3]  Lennart Ljung,et al.  A statistical perspective on state-space modeling using subspace methods , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

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

[5]  B. Gopinath.  On the identification of linear time-invariant systems from input-output data , 1969 .

[6]  H. Akaike.  A new look at the statistical model identification , 1974 .

[7]  Lennart Ljung,et al.  A Study of Some Approaches to Vibration Data Analysis , 1994 .

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

[9]  K. Glover.  All optimal Hankel-norm approximations of linear multivariable systems and their L, ∞ -error bounds† , 1984 .

[10]  L. Ljung,et al.  Design variables for bias distribution in transfer function estimation , 1986, The 23rd IEEE Conference on Decision and Control.

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

[12]  D. S. Bayard,et al.  An algorithm for state-space frequency domain identification without windowing distortions , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

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

[14]  H. Zeiger,et al.  Approximate linear realizations of given dimension via Ho's algorithm , 1974 .

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

[16]  Michel Verhaegen,et al.  Application of a subspace model identification technique to identify LTI systems operating in closed-loop , 1993, Autom..

[17]  Johan A. K. Suykens,et al.  Subspace algorithms for system identification and stochastic realization , 1991 .

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

[19]  D. Lainiotis,et al.  System identification : advances and case studies , 1976 .

[20]  Thomas Kailath,et al.  Fast subspace decomposition , 1994, IEEE Trans. Signal Process..

[21]  Mats Viberg,et al.  Subspace Methods in System Identification , 1994 .

[22]  T. W. Anderson.  An Introduction to Multivariate Statistical Analysis , 1959 .

[23]  Lennart Ljung,et al.  A simple start-up procedure for canonical form state space identification, based on subspace approximation , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[24]  Thomas Kailath,et al.  Linear Systems , 1980 .

[25]  T. McKelvey.  Identification of State-Space Models from Time and Frequency Data , 1995 .

[26]  M. Moonen,et al.  QSVD approach to on- and off-line state-space identification , 1990 .

[27]  Lennart Ljung,et al.  On-line structure selection for multivariable state-space models , 1982, Autom..

[28]  Petre Stoica,et al.  MUSIC, maximum likelihood, and Cramer-Rao bound , 1989, IEEE Transactions on Acoustics, Speech, and Signal Processing.

[29]  Marc Moonen,et al.  Comments on 'State-space model identification with data correlation’ , 1992 .

[30]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[31]  Thomas Kailath,et al.  Fast recursive identification of state space models via exploitation of displacement structure , 1994, Autom..

[32]  Michel Verhaegen,et al.  A Novel Non-Iterative Mimo State Space Model Identification Technique , 1991 .

[33]  H. Hotelling.  Analysis of a complex of statistical variables into principal components. , 1933 .

[34]  R. O. Schmidt,et al.  Multiple emitter location and signal Parameter estimation , 1986 .

[35]  K. Liu,et al.  Identification and Control of NASA's ACES Structure , 1991, 1991 American Control Conference.

[36]  Lennart Ljung,et al.  Efficient Construction of Transfer Functions from Frequency Response Data , 1994 .

[37]  Β. L. HO,et al.  Editorial: Effective construction of linear state-variable models from input/output functions , 1966 .

[38]  U. B. Desai,et al.  A Generalized Approach to q-Markov Covariance Equivalent Realizations for Discrete Systems , 1987, 1987 American Control Conference.

[39]  Petre Stoica,et al.  Weighted LS and TLS approaches yield asymptotically equivalent results , 1995, Signal Process..

[40]  Raman K. Mehra.  A New Unified Approach to State Space Model Strucuture Determination and Maximum Likelihood Identification with Aerospace Applications , 1994 .

[41]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[42]  V. Pisarenko.  The Retrieval of Harmonics from a Covariance Function , 1973 .

[43]  Robert E. Skelton,et al.  Identification of Linear Systems from their Pulse Responses , 1992, 1992 American Control Conference.

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

[45]  M. Moonen,et al.  On- and off-line identification of linear state-space models , 1989 .

[46]  P. Overschee.  Subspace Identification: Theory, Implementation, Application , 1995 .

[47]  Bhaskar D. Rao,et al.  Model based processing of signals: a state space approach , 1992, Proc. IEEE.

[48]  Björn E. Ottersten,et al.  Analysis of subspace fitting and ML techniques for parameter estimation from sensor array data , 1992, IEEE Trans. Signal Process..

[49]  Ruud J.P. Schrama,et al.  An Open-loop Solution to the Approximate Closed-loop Identification Problem , 1991 .

[50]  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.

[51]  Sun-Yuan Kung,et al.  A new identification and model reduction algorithm via singular value decomposition , 1978 .

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

[53]  Petre Stoica,et al.  Maximum likelihood methods for direction-of-arrival estimation , 1990, IEEE Trans. Acoust. Speech Signal Process..

[54]  B. Moor,et al.  A geometrical strategy for the identification of state space models of linear multivariable systems with singular value decomposition , 1987 .

[55]  Yucai Zhu,et al.  Comparison of Three Classes of Identification Methods , 1994 .

[56]  Björn E. Ottersten,et al.  Sensor array processing based on subspace fitting , 1991, IEEE Trans. Signal Process..

[57]  Lennart Ljung,et al.  Performance of Subspace-Based System Identification Methods , 1993 .

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

[59]  K. Liu.  Identification of multi-input multi-output systems by observability range space extraction , 1992, [1992] Proceedings of the 31st IEEE Conference on Decision and Control.

[60]  Paul M. J. Van den Hof,et al.  An indirect method for transfer function estimation from closed loop data , 1993, Autom..

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

[62]  Bhaskar D. Rao,et al.  Performance analysis of ESPRIT and TAM in determining the direction of arrival of plane waves in noise , 1989, IEEE Trans. Acoust. Speech Signal Process..

[63]  Bjorn Ottersten,et al.  A Subspace Based Instrumental Variable Method for State-Space System Identification , 1994 .

[64]  Masanao Aoki,et al.  State Space Modeling of Time Series , 1987 .

[65]  Jer-Nan Juang,et al.  An eigensystem realization algorithm for modal parameter identification and model reduction. [control systems design for large space structures] , 1985 .

[66]  A. Swindlehurst,et al.  Subspace-based signal analysis using singular value decomposition , 1993, Proc. IEEE.

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