# RECURSIVE MOESP TYPE SUBSPACE IDENTIFICATION ALGORITHM

### Catarina J. M. Delgado, P. Lopes dos Santos

#### Abstract

In this paper two recursive algorithms, based on MOESP type subspace identification, are presented in two versions. The main idea was to show that we can represent subspace identification methods as sequences of least squares problems and implement them through sequences of modified Householder algorithms. Therefore, it is possible to develop iterative algorithms with most of the advantages of this kind of methods, and still improve the numerical efficiency, in order to deal with real-time applications and minimize the computational burden.

#### References

- Chiuso, A. and Picci, G. (2001). Asymptotic variance of subspace estimates. In Proc. CDC'01 - 40th Conference on Decision and Control, Orlando, Florida, USA, pages 3910-3915.
- Cho, Y., Xu, G., and Kailath, T. (1994). Fast recursive identi cation of state space models via exploitation of displacement structure. Automatica, 30:45-59.
- Delgado, C. and dos Santos, P. L. (2004a). Analysis and ef ciency improvement of the estimation of matrices a and c in some subspace identi cation methods. In Proc. SICPRO'05 - 4th International Conference on System Identi cation and Control Problems, Moscow, Russia (Accepted for Publication).
- Delgado, C. and dos Santos, P. L. (2004b). Exploring the linear relations in the estimation of matrices b and d in subspace identi cation methods. In Proc. ICINCO'04 - 1st International Conference on Informatics in Control, Automation and Robotics, Set úbal, Portugal.
- dos Santos, P. L. and de Carvalho, J. L. M. (2003). Improving the numerical ef ciency of the b and d estimates produced by the combined deterministic-stochastic subspace identi cation algorithms. In Proc. CDC'03 - 42nd Conference on Decision and Control, Maui, Hawaii, USA, pages 3473-3478.
- dos Santos, P. L. and de Carvalho, J. L. M. (2004). A new insight to the a and c matrices extraction in a MOESP type subspace identi cation algorithm. In Proc. Controlo'04 - 6th Portuguese Conference on Automatic Control, Faro, Portugal.
- Golub, G. and van Loan, C. (1996). Matrix Computations. Johns Hopkins University Press, 3rd edition.
- Gustafsson, T., Lovera, M., and Verhaegen, M. (1998). A novel algorithm for recursive instrumental variable based subspace identi cation. In Proc. CDC'98, Conference on Decision and Control, pages 3920-3925.
- Larimore, W. (1990). Canonical variate analysis in identi - cation, ltering and adaptive control. In Proc. CDC'90 - 29th Conference on Decision and Control, pages 596-604.
- Ljung, L. (1983). Theory and Practice of Recursive Identication. The MIT Press.
- Ljung, L. (1987). System Identi cation: Theory for the User. Prentice-Hall.
- Moonen, M., de Moor, B., Vandenberghe, L., and Vandewalle, J. (1989). On- and off-line identi cation of linear state space models. International Journal of Control, 49:219-232.
- Oku, H. and Kimura, H. (2000). Recursive algorithms of the state-space subspace system identi cation. Automatica.
- van Overschee, P. and de Moor, B. (1996). Subspace Identi cation for linear systems. Kluwer Academic Publishers.
- Verhaegen, M. (1994). Identi cation of the deterministic part of MIMO state space models given in innovations form from input-output data. Automatica, 30:61-74.
- Viberg, M., Ottersten, B., Wahlberg, B., and Ljung, L. (1991). Performance of subspace based state-space systems identi cation methods. In Proc. IFAC'91 - 12th IFAC World Congress, Sydney, Australia.

#### Paper Citation

#### in Harvard Style

Delgado C. and dos Santos P. (2004). **RECURSIVE MOESP TYPE SUBSPACE IDENTIFICATION ALGORITHM** . In *Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,* ISBN 972-8865-12-0, pages 176-182. DOI: 10.5220/0001146801760182

#### in Bibtex Style

@conference{icinco04,

author={Catarina J. M. Delgado and P. Lopes dos Santos},

title={RECURSIVE MOESP TYPE SUBSPACE IDENTIFICATION ALGORITHM},

booktitle={Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,},

year={2004},

pages={176-182},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001146801760182},

isbn={972-8865-12-0},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Informatics in Control, Automation and Robotics - Volume 3: ICINCO,

TI - RECURSIVE MOESP TYPE SUBSPACE IDENTIFICATION ALGORITHM

SN - 972-8865-12-0

AU - Delgado C.

AU - dos Santos P.

PY - 2004

SP - 176

EP - 182

DO - 10.5220/0001146801760182