Abstract
An overview is given of the class of subspace techniques (STs) for identifying linear, time-invariant state-space models from input-output data. STs do not require a parametrization of the system matrices and as a consequence do not suffer from problems related to local minima that often hamper successful application of parametric optimization- based identification methods.
The overview follows the historic line of development. It starts from Kronecker’s result on the representation of an infinite power series by a rational function and then addresses, respectively, the deterministic realization problem, its stochastic variant, and finally the identification of a state-space model given in innovation form.
The overview summarizes the fundamental principles of the algorithms to solve the problems and summarizes the results about the statistical properties of the estimates as well as the practical issues like choice of weighting matrices and the selection of dimension parameters in using these STs in practice. The overview concludes with probing some future challenges and makes suggestions for further reading.
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Bibliography
Bauer D (2005) Asymptotic properties of subspace estimators. Automatica 41(3):359–376
Bauer D, Ljung L (2002) Some facts about the choice of the weighting matrices in larimore type of subspace algorithms. Automatica 38(5):763–773
Cauberghe B, Guillaume P, Pintelon R, Verboven P (2006) Frequency-domain subspace identification using {FRF} data from arbitrary signals. J Sound Vib 290(3–5):555–571
Chiuso A (2010) Asymptotic properties of closed-loop cca-type subspace identification. IEEE-TAC 55(3):634–649
Jansson M, Wahlberg B (1996) A linear regression approach to state-space subspace systems. Signal Process 52:103–129
Juang J-N, Pappa RS (1985) Approximate linear realizations of given dimension via Ho’s algorithm. J Guid Control Dyn 8(5):620–627
Katayama T (2005) Subspace methods for system identification. Springer, London
Kronecker L (1890) Algebraische reduktion der schaaren bilinearer formen. S.B. Akad. Berlin, pp 663–776
Larimore W (1990) Canonical variate analysis in identification, filtering, and adaptive control. In: Proceedings of the 29th IEEE conference on decision and control, 1990, Honolulu, vol 2, pp 596–604
Liu Z, Vandenberghe L (2010) Interior-point method for nuclear norm approximation with application to system identification. SIAM J Matrix Anal Appl 31(3):1235–1256
Ljung L (2007) The system identification toolbox: the manual. The MathWorks Inc., Natick. 1st edition 1986, 7th edition 2007
Peternell K, Scherrer W, Deistler M (1996) Statistical analysis of novel subspace identification methods. Signal Process 52(2):161–177
Schutter BD (2000) Minimal state space realization in linear system theory: an overview. J Comput Appl Math 121(1–2):331–354
van der Veen GJ, van Wingerden JW, Bergamasco M, Lovera M, Verhaegen M (2013) Closed-loop subspace identification methods: an overview. IET Control Theory Appl 7(10):1339–1358
Van Overschee P, De Moor B (1993) Subspace algorithms for the stochastic identification problem. Automatica 29(3):649–660
Van Overschee P, De Moor B (1994) N4sid: subspace algorithms for the identification of combined deterministic-stochastic systems. Automatica 30(1):75–93
Van Overschee P, De Moor B (1995) A unifying theorem for three subspace system identification algorithms. Automatica 31(12):1853–1864
Van Overschee P, De Moor B (1996) Identification for linear systems: theory – implementation – applications. Kluwer Academic Publisher Group, Dordrecht
van Wingerden J, Verhaegen M (2009) Subspace identification of bilinear and LPV systems for open and closed loop data. Automatica 45(2):372–381
Verhaegen M (1994) Identification of the deterministic part of mimo state space models given in innovations form from input–output data. Automatica 30(1):61–74
Verhaegen M, Verdult V (2007) Filtering and identification: a least squares approach. Cambridge University Press, Cambridge/New York
Verhaegen M, Yu X (1995) A class of subspace model identification algorithms to identify periodically and arbitrarily time-varying systems. Automatica 31(2):201–216
Viberg M (1995) Subspace-based methods for the identification of linear time-invariant systems. Automatica 31(12):1835–1851
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© 2014 Springer-Verlag London
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Verhaegen, M. (2014). Subspace Techniques in System Identification. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_107-1
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DOI: https://doi.org/10.1007/978-1-4471-5102-9_107-1
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Latest
Subspace Techniques in System Identification- Published:
- 08 November 2019
DOI: https://doi.org/10.1007/978-1-4471-5102-9_107-2
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Original
Subspace Techniques in System Identification- Published:
- 18 March 2014
DOI: https://doi.org/10.1007/978-1-4471-5102-9_107-1