Identification of MIMO Hammerstein systems with non-linear feedback

Subspaceidentification algorithms are proposed in this paper for a class of multi-input multi-output (MIMO) discrete-time closed-loop Hammerstein systems. In particular, instrumental variable (IV) techniques are applied to solve the correlations between the input signals and the signals that are fed back into the system. An augmented IV identification approach is introduced to address a problem related to the application of the numerical efficient RQ decomposition algorithm to a rank-decreased correlation matrix. The contribution of this paper is to provide a unified approach to identify a class of non-linear closed-loop systems and solve the related numerical issues during the implementation. Analysis and numerical examples are presented to demonstrate the validity of the algorithms proposed in this paper.

[1]  A. Leonessa,et al.  Nonlinear identification of marine thruster dynamics , 2001, MTS/IEEE Oceans 2001. An Ocean Odyssey. Conference Proceedings (IEEE Cat. No.01CH37295).

[2]  P. V. D. Hof,et al.  System identification with generalized orthonormal basis functions , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[3]  T. Markham,et al.  Schur complements of diagonally dominant matrices , 1979 .

[4]  Björn E. Ottersten,et al.  Array processing in correlated noise fields based on instrumental variables and subspace fitting , 1995, IEEE Trans. Signal Process..

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

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

[7]  Tony Gustafsson.  Subspace identification using instrumental variable techniques , 2001, Autom..

[8]  Bart De Moor,et al.  Continuous-time frequency domain subspace system identification , 1996, Signal Process..

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

[10]  K. Arun,et al.  Balanced approximation of stochastic systems , 1990 .

[11]  Bo Wahlberg,et al.  On Consistency of Subspace Methods for System Identification , 1998, Autom..

[12]  Dennis S. Bernstein,et al.  Subspace identification for nonlinear systems that are linear in unmeasured states , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[13]  K. Åström.  Introduction to Stochastic Control Theory , 1970 .

[14]  B. Moor,et al.  Subspace identification for linear systems , 1996 .

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

[16]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

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

[18]  Lennart Ljung,et al.  Subspace identification from closed loop data , 1996, Signal Process..

[19]  John F. MacGregor,et al.  A framework for subspace identification methods , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[20]  J. B. Gomm,et al.  Experiment design considerations for non-linear system identification using neural networks , 1997 .

[21]  B. Moor,et al.  Closed loop subspace system identification , 1997 .