A unifying theorem for three subspace system identification algorithms

The aim of this paper is to indicate the striking similarities between three different subspace algorithms for the identification of combined deterministic-stochastic systems. The similarities between these algorithms have been obscured, due to different notations and backgrounds. It is shown that all three algorithms are special cases of one unifying theorem. The comparison also indicates that the three algorithms use exactly the same subspace to determine the order and the extended observability matrix, but the weighting of the space is different in the three cases.

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

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

[3]  Bart De Moor,et al.  Choice of state-space basis in combined deterministic-stochastic subspace identification , 1995, Autom..

[4]  L. Ljung,et al.  Performance of Subspace Based State-Space System Identification Methods , 1993 .

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

[6]  T. Kailath,et al.  A subspace rotation approach to signal parameter estimation , 1986, Proceedings of the IEEE.

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

[8]  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.

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

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

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

[12]  H. Akaike.  Markovian Representation of Stochastic Processes by Canonical Variables , 1975 .

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

[14]  B. Anderson,et al.  Model reduction for control system design , 1984 .