Subspace model identification Part 1. The output-error state-space model identification class of algorithms

In this paper, we present two novel algorithms to realize a finite dimensional, linear time-invariant state-space model from input-output data. The algorithms have a number of common features. They are classified as one of the subspace model identification schemes, in that a major part of the identification problem consists of calculating specially structured subspaces of spaces defined by the input-output data. This structure is then exploited in the calculation of a realization. Another common feature is their algorithmic organization: an RQ factorization followed by a singular value decomposition and the solution of an overdetermined set (or sets) of equations. The schemes assume that the underlying system has an output-error structure and that a measurable input sequence is available. The latter characteristic indicates that both schemes are versions of the MIMO Output-Error State Space model identification (MOESP) approach. The first algorithm is denoted in particular as the (elementary MOESP scheme)...

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

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

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

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

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

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

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

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

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

[10]  P. Caines.  Linear Stochastic Systems , 1988 .

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

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

[13]  M. Kreĭn,et al.  ANALYTIC PROPERTIES OF SCHMIDT PAIRS FOR A HANKEL OPERATOR AND THE GENERALIZED SCHUR-TAKAGI PROBLEM , 1971 .

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

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

[16]  L.-C. Suen,et al.  Minimal dimension realization versus minimal realization and a correction to "Minimal dimension realization and identifiability of input-output sequences" , 1977, IEEE Transactions on Automatic Control.

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