On consistency of output-error closed-loop subspace model identification for systems compensated by general LTI controllers

Abstract This paper deals with consistency analysis of a closed-loop subspace model identification method for systems compensated by general linear time-invariant feedback controllers. The results presented here are a straightforward extension from the authors’ recent work for systems compensated with constant gain feedback controllers. It is shown that the estimate of the extended observability matrix, which is obtained from our closed-loop subspace model identification method, is consistent up to a similarity transform.

[1]  H. Akaike.  Canonical Correlation Analysis of Time Series and the Use of an Information Criterion , 1976 .

[2]  Hiroshi Oku,et al.  MOESP-type Closed-loop Subspace Model Identification Method , 2006 .

[3]  Hiroshi Oku,et al.  On error analysis of a closed-loop subspace model identification method , 2021, IFAC-PapersOnLine.

[4]  Hiroshi Oku.  Asymptotic Property of MOESP-type Closed-loop Subspace Model Identification , 2010 .

[5]  Alessandro Chiuso,et al.  The role of vector autoregressive modeling in predictor-based subspace identification , 2007, Autom..

[6]  Hiroshi Oku,et al.  Direct subspace model identification of LTI systems operating in closed-loop , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[7]  Lennart Ljung,et al.  Some facts about the choice of the weighting matrices in Larimore type of subspace algorithms , 2002, Autom..

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

[9]  Shun Ushida,et al.  MIMO closed-loop subspace model identification and hovering control of a 6-DOF coaxial miniature helicopter , 2014, 2014 Proceedings of the SICE Annual Conference (SICE).

[10]  Dietmar Bauer,et al.  Analysis of the asymptotic properties of the MOESP type of subspace algorithms , 2000, Autom..

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

[12]  M. Jansson.  Asymptotic Variance Analysis of Subspace Identification Methods , 2000 .

[13]  Alessandro Chiuso.  Asymptotic variance of closed-loop subspace identification methods , 2006, IEEE Transactions on Automatic Control.

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

[15]  Alessandro Chiuso,et al.  Consistency analysis of some closed-loop subspace identification methods , 2005, Autom..

[16]  An Estimation Method of Innovations Model in Closed-Loop Environment with Lower Horizons , 2020 .

[17]  Shun Ushida,et al.  An Experiment on Closed-loop System Identification of UAV Using Dual-rate Sampling , 2018 .

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

[19]  Magnus Jansson,et al.  Subspace Identification and ARX Modeling , 2003 .

[20]  Dietmar Bauer,et al.  Consistency and asymptotic normality of some subspace algorithms for systems without observed inputs , 1999, Autom..

[21]  Kenji Ikeda.  On the precision of the plant estimates in some subspace identification methods , 2014 .

[22]  Alessandro Chiuso,et al.  On the Asymptotic Properties of Closed-Loop CCA-Type Subspace Algorithms: Equivalence Results and Role of the Future Horizon , 2010, IEEE Transactions on Automatic Control.