Some algorithmic aspects of subspace identificationwith inputs

• Autorzy: Alessandro Chiuso , Giorgio Picci
• Języki publikacji: EN

Abstrakty

EN

It has been experimentally verified that most commonly used subspace methods for identification of linear state-space systems with exogenous inputs may, in certain experimental conditions, run into ill-conditioning and lead to ambiguous results. An analysis of the critical situations has lead us to propose a new algorithmic structure which could be used either to test difficult cases andor to implement a suitable combination of new and old algorithms presented in the literature to help fixing the problem.

Słowa kluczowe

EN

ill-conditioning; multivariable systems; identification with inputs; subspace identification

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2001
• Tom: 11
• Numer: 1
• Strony: 55-75

Daty

wydano

2001

otrzymano

2000-09-01

poprawiono

2001-01-01

Twórcy

autor

Alessandro Chiuso

• Dipartimento di Elettronica e Informatica, Universita di Padova, 35131 Padua, Italy

autor

Giorgio Picci

• Dipartimento di Elettronica e Informatica, Universita di Padova, 35131 Padua, Italy

Bibliografia

• Akaike H. (1974): Stochastic theory of minimal realization. -IEEE Trans. Automat. Contr., Vol.AC-19, No.6,pp.667-674.
• Akaike H. (1975): Markovian representation of stochastic processes by canonical variables. - SIAM J. Contr., Vol.13, No.1, pp.162-173.
• Akaike H. (1976): Canonical correlation analysis of time series andthe use of an information criterion, In: System Identification: Advances and Case Studies (R. Mehra and D. Lainiotis, Eds.). - New York: Academic Press,pp.27-96.
• Aoki M. (1990): State Space Modeling of Time Series, 2nd Ed. -Berlin: Springer.
• Bauer D. (1998): Some asymptotic theory for the estimation of linear systemsusing maximum likelihood methods or subspace algorithms. - Ph.D.Thesis, TU Wien.
• Bauer D. (2000): Asymptotic efficiency of the CCA subspace method in thecase of no exogenous inputs. - (submitted).
• Bauer D. and Jansson M. (2000): Analysis of the asymptotic properties of the moesp type ofsubspace algorithms. - Automatica, Vol.36, No.4, pp.497-509.
• Bittanti S. and Lovera M. (1998): Assessing Model Uncertainty in Subspace Identification Methods: a Simulation Study, In: Proc. MTNS-98 (A. Beghi, L. Finesso, G. Picci, Eds.). - Padova: Il Poligrafo, pp.703-706.
• Chiuso A. (2000): Geometric methods for subspace identifcation. - Ph.D. Thesis,Department of Electronics and Informatics, University of Padova, Italy.
• Chiuso A. and Picci G. (1999): Subspace identification by orthogonal decomposition. -Proc. 14th IFAC World Congress, Beijing, China, Vol.I, pp.241-246.
• Chiuso A. and Picci G. (2000a): Error analysis of certain subspace methods. -Proc. SYSID 2000, S. Barbara, CA, Session No.WEAM3-1 (on CD-ROM).
• Chiuso A. and Picci G. (2000b): Probing inputs for subspace identification. - Proc. 39th Conf. Decision and Control, Sydney, Australia, CA, pp.1544-1549.
• Chiuso A. and Picci G. (2000c): On the ill-conditioning of certain subspace identification methods with inputs. - (in preparation).
• Chou T. and Verhaegen M. (1997): Subspace algorithms for the identification ofmultivariable dynamic errors-in-variables models. - Automatica, Vol.33,No.10, pp.1857-1869.
• Faurre P. (1976): Stochastic realization algorithms,In: System Identification: Advances and Case Studies (R. Mehra and D. Lainotis,Eds.). - New York: Academic Press.
• Guidorzi R.P. (1981): Invariants and canonical forms for systems: structural andparameter identification. - Automatica, Vol.17, No.1, pp.117-133.
• Ho B.L. and Kalman R.E. (1966): Effective construction of linearstate-variable models from inputoutput functions. - Regelungstechnik, Vol.14, No.12, pp.545-548.
• Hotelling H. (1936): Relations between two sets of variables. - Biometrika, Vol.28, No.3, pp.321-377.
• Jansson M. and Wahlberg B. (1997): Counterexample to the general consistency of subspace system identification metods. -Proc. SYSID 97, Fukuoka, Japan, pp.1677-1682.
• Kawauchi H., Chiuso A., Katayama T. and Picci G. (1999): Comparison of two subspaceidentification methods for combined deterministic-stochasticsystems. - Proc. 31st ISCIE Int. Symp.s Stochastic Systems Theory and its Applications, Yokohama, Japan, pp.7-12.
• Katayama T. and Picci G. (1999): Realization of stochastic systems with exogenousinputs and subspace system identification methods. - Automatica, Vol.35, No.10, pp.1635-1652.
• Katayama T., Omori T. and Picci T. (1998): Comparison of some subspace identification methods. - Proc. Conf. Decision and Control, Tampa, Florida, pp.1850-1852.
• Larimore W.E. (1983): System identification, reduced-order filtering and modeling viacanonical variate analysis. -Proc. American Control Conf., San Francisco, CA, pp.445-451.
• Larimore W.E. (1990): Canonical variate analysis inidentification, filtering, and adaptive control. - Proc. 29th IEEE Conf. Decision and Control, Honolulu, pp.596-604.
• Lindquist A. and Pavon M. (1984): On the structure of state space models of discrete-time vector processes. - IEEE Trans. Automat. Contr., Vol.AC-29,No.5, pp.418-432.
• Lindquist A. and Picci G. (1979): On the stochastic realization problem. -SIAM J. Contr. Optim., Vol.17, No.3, pp.365-389.
• Lindquist A. and Picci G. (1991): A geometric approach to modelling and estimation of linear stochasticsystems. -J. Math. Syst. Estim. Contr., Vol.1, No.3, pp.241-333.
• Lindquist A. and Picci G. (1996a): Canonical correlation analysisapproximate covariance extension and identification of stationary timeseries. - Automatica, Vol.32, No.5, pp.709-733.
• Lindquist A. and Picci G. (1996b): Geometric methods for state spaceidentification, In: Identification, Adaptation, Learning, (Lectures given at the NATO-ASI School, From Identifiation to Learning held in Como, Italy). - Berlin: Springer.
• Lindquist A., Picci G. and Ruckebusch G. (1979): On minimal splitting subspaces and Markovian representation. -Math. Syst. Theory, Vol.12, pp.271-279.
• Ljung L. (1987): System Identification-Theory for the User. -Englewood Cliffs, NJ: Prentice-Hall.
• Lovera M. (1997): Subspace metods: Theory and applications. - Ph.D. Thesis, Politecnico di Milano.
• Moonen M. and Vandewalle J. (1990): QSVD Approach to on- and off-linestate-space identification. - Int. J. Contr., Vol.51, No.5, pp.1133-1146.
• Moonen M., De Moor B., Vanderberghe L. and Vandewalle J. (1989): On- and off-line identification of linear state-space models. -Int. J. Contr., Vol.49, No.1, pp.219-232.
• Ober R.J. (1996): Balanced canonical forms, In: Identification,Adaptation, Learning, (Lectures given at the NATO-ASI School,e From Identifiation to Learning held in Como, Italy,Aug.1994), Berlin: Springer.
• Peternell K. (1995): Identification of linear time-invariant systems viasubspace and realization-based methods. - Ph.D. Thesis, TU Wien.
• Peternell K., Scherrer W. and Deistler M. (1996): Statisticalanalysis of novel subspace identification methods. - Signal Process., Vol.52, No.2, pp.161-177.
• Picci G. (1976): Stochastic realization of Gaussianprocesses. - Proc. IEEE, Vol.64, No.1, pp.112-122.
• Picci G. (1996): Geometric Methods in Stochastic Realization and System Identification. -CWI Quarterly, Special Issue on System Theory, Vol.9, No.3,pp.205-240.
• Picci G. (1997a): Stochastic realization and system identification, In: Statistical Methods in Control and Signal Processing (T. Katayama and I. Sugimoto,Eds.). - New York: M. Dekker.
• Picci G. (1997b): Oblique splitting susbspaces and stochastic realization withinputs, In: Operators, Systems and Linear Algebra (U. Helmke, D. Pratzel-Woltersand E. Zerz, Eds.). - Stuttgart: Teubner, pp.157-174.
• Picci G. (1997c): Statistical properties of certain subspace identificationmethods, Proc. SYSID 97, Fukuoka, Japan, Vol.3, pp.1093-1099.
• Picci G. and Katayama T. (1996a): A simple 'subspace' identification algorithm with exogenous inputs. -Proc. Triennial IFAC Congress, San Francisco, CA, Vol.I, pp.175-180.
• Picci G. and Katayama T. (1996b): Stochastic realization with exogenous inputs and 'Subspace Methods' Identification. - Signal Process., Vol.52, No.2, pp.145-160.
• Ruckebusch G. (1976): Representations markoviennes de processus gaussiensstationnaires. - C.R. Acad. Sc. Paris, Series A, Vol.282, pp.649-651.
• Ruckebusch G. (1978): A state space approach to the stochastic realization problem. -Proc. 1978 IEEE Int. Symp. Circuits and Systems, New York, pp.972-977.
• Stoica P. and Viberg M. (1995): Weighted LS and TLS approaches yields asympotically equivalentresults. -Signal Process., Vol.45, No.2, pp.255-259.
• Van Overschee P. and De Moor B. (1993): Subspacealgorithms for the stochastic identification problem. - Automatica, Vol.29,No.3, pp.649-660.
• Van Overschee P. and De Moor B. (1994): N4SID: Subspace algorithms for the identification of combineddeterministic-stochastic systems. - Automatica, Vol.30, No.1, pp.75-93.
• Van Overschee P. and De Moor B. (1996): Subspace Identificationfor Linear Systems. - Dordrecht: Kluwer.
• Verhaegen M. (1993): Application of a subspace model identification technique toidentify LTI systems operating in closed-loop. - Automatica, Vol.29,No.4, pp.1027-1040.
• Verhaegen M. (1994): Identification of thedeterministic part of MIMO state space models given in innovations form frominput-output data. - Automatica, Vol.30, No.1, pp.61-74.
• Verhaegen M. and Dewilde P. (1992): Subspace model identification,Part 1. The output-error state-space model identification class of algorithms; Part 2.Analysis of the elementary output-error state-space model identification algorithm. -Int. J. Contr., Vol.56, No.5, pp.1187-1210; 1211-1241.
• Viberg M. (1995): Subspace-based methods for the identification oflinear time-invariant systems. - Automatica, Vol.31, No.3, pp.1835-1851.