15th Triennial World Congress of the International Federation of Automatic Control
  Barcelona, 21–26 July 2002 
SUBSPACE IDENTIFICATION OF CLOSED LOOP SYSTEMS BY STOCHASTIC REALIZATION
Tohru KATAYAMA* Hidetoshi KAWAUCHI* Giorgio PICCI**
* Department of Applied Mathematics and Physics
Graduate School of Informatics, Kyoto University, Kyoto, 606-8501,
Japan; katayama@amp.i.kyoto-u.ac.jp
** Dipartimento di Elettronica e Informatica
University of Padova, 35131 Padova, Italy; picci@dei.unipd.it

We develop a closed loop subspace identification method based on stochastic realization theory. Using the preliminary orthogonal decomposition of (Picci and Katayama, 1996b) we show that, under the assumption that the exogenous input is feedback-free and persistently exciting (PE), the identification of closed loop systems is divided into two subproblems: the deterministic identification of the plant and controller, and the stochastic identification of the noise filter. Subspace methods for identifying the deterministic and stochastic parts are derived by adapting the standard subspace methods to the deterministic and stochastic components. In both cases, a model reduction procedure should be applied in order to extract controllable and observable parts from non-minimal realizations. Some numerical results are included to show the applicability of the present technique.
Keywords: Closed loop systems, Subspace methods, Stochastic Realization, LQ decomposition
Session slot T-Mo-M02: State Space Identification and Subspace Methods/Area code 3a : Modelling, Identification and Signal Processing