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2015 | OriginalPaper | Chapter

17. Stochastic Systems with Inputs

Authors : Anders Lindquist, Giorgio Picci

Published in: Linear Stochastic Systems

Publisher: Springer Berlin Heidelberg

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Abstract

In this chapter we study the stochastic realization problem with inputs. Our aim is to provide procedures for constructing state space models for a stationary process y driven by an exogenous observable input signal u, also modeled as a stationary process.

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previous chapter Acausal Linear Stochastic Models and Spectral Factorization
Footnotes
1
Here the explicit computation of the update \(\Omega _{\nu -1}^{\dag }\hat{Y }_{[t+1,T]}\) can be avoided using instead a “shift-invariance” argument on the estimated observability matrix, see Sect. 13.​3.
 
2
“Complementary”, since it is the orthogonal complement of U [t, T] in the data space \(Z_{[t_{0},t)} \vee U_{[t,T]}\). The notation \(U_{[t,T]}^{\perp }\) is not completely consistent since the ambient space of the complement varies with t.
 
3
Recall that strict stability of the predictor is always required for prediction error methods [212].
 
4
Here the system order n is also assumed to be known. Of course any consistent order estimation procedure used in subspace identification would serve to the purpose. Order estimation is performed in most subspace identification algorithms by a (weighted) SVD truncation step which was discuss in the previous subsection.
 
Literature
11.
Anderson, B.D.O., Gevers, M.R.: Identifiability of linear stochastic systems operating under linear feedback. Automatica 18(2), 195–213 (1982)CrossRefMATHMathSciNet
26.
49.
50.
Caines, P.E., Chan, C.W.: Estimation, identification and feedback. In: Mehra, R., Lainiotis, D. (eds.) System Identification: Advances and Case Studies, pp. 349–405. Academic, New York (1976)CrossRef
53.
Chiuso, A.: On the relation between cca and predictor-based subspace identification. IEEE Trans. Autom. Control 52(10), 1795–1812 (2007)CrossRefMathSciNet
54.
Chiuso, A., Picci, G.: Probing inputs for subspace identification (invited paper). In: Proceedings of the 2000 Conference on Decision and Control, pages paper CDC00–INV0201, Sydney, Dec 2000
55.
Chiuso, A., Picci, G.: Geometry of oblique splitting, minimality and Hankel operators. In: Rantzer, A., Byrnes, C. (eds.) Directions in Mathematical Systems Theory and Optimization. Number 286 in Lecture Notes in Control and Information Sciences, pp. 85–124. Springer, New York (2002)
56.
57.
Chiuso, A., Picci, G.: Asymptotic variance of subspace methods by data orthogonalization and model decoupling: a comparative analysis. Automatica 40(10), 1705–1717 (2004)CrossRefMATHMathSciNet
58.
59.
Chiuso, A., Picci, G.: Subspace identification by data orthogonalization and model decoupling. Automatica 40(10), 1689–1703 (2004)CrossRefMATHMathSciNet
60.
Chiuso, A., Picci, G.: Consistency analysis of some closed-loop subspace identification methods. Autom.: Spec. Issue Syst. Identif. 41, 377–391 (2005)
61.
Chiuso, A., Picci, G.: Constructing the state of random processes with feedback. In: Proceedings of the IFAC International Symposium on System Identification (SYSID-03), Rotterdam, Aug 2003
115.
Gevers, M.R., Anderson, B.D.O.: Representations of jointly stationary stochastic feedback processes. Int. J. Control 33(5), 777–809 (1981)CrossRefMATHMathSciNet
116.
Gevers, M.R., Anderson, B.D.O.: On jointly stationary feedback-free stochastic processes. IEEE Trans. Autom. Control 27, 431–436 (1982)CrossRefMATH
123.
149.
167.
Katayama, T., Kawauchi, H., Picci, G.: Subspace identification of closed loop systems by orthogonal decomposition. Automatica 41, 863–872 (2005)CrossRefMATHMathSciNet
168.
Katayama, T., Picci, G.: Realization of stochastic systems with exogenous inputs and subspace system identification methods. Automatica 35(10), 1635–1652 (1999)CrossRefMATHMathSciNet
178.
Larimore, W.E.: System identification, reduced-order filtering and modeling via canonical variate analysis. In: Proceedings of the American Control Conference, San Francisco, pp. 445–451 (1983)
212.
Ljung, L.: System Identification; Theory for the User, 2nd edn. Prentice Hall, Upper Saddle River (1999)
251.
Picci, G.: Oblique splitting subspaces and stochastic realization with inputs. In: Prätzel-Wolters, D., Helmke, U., Zerz, E. (eds.) Operators, Systems and Linear Algebra, pp. 157–174. Teubner, Stuttgart (1997)CrossRef
252.
Picci, G.: Stochastic realization and system identification. In: Katayama, T., Sugimoto, I. (eds.) Statistical Methods in Control and Signal Processing, pp. 205–240. M. Dekker, New York (1997)
255.
Picci, G., Katayama, T.: Stochastic realization with exogenous inputs and “subspace methods” identification. Signal Process. 52, 145–160 (1996)CrossRefMATH
260.
Qin, S.J., Ljung, L.: Closed-loop subspace identification with innovation estimation. In: Proceedings of SYSID 2003, Rotterdam, Aug 2003
294.
van Overschee, P., De Moor, B.: N4SID: subspace algorithms for the identification of combined deterministic-stochastic systems. Automatica 30, 75–93 (1994)CrossRefMATH
295.
Van Overschee, P., De Moor, B.: Choice of state-space basis in combined deterministic-stochastic subspace identification. Automatica 31(12), 1877–1883 (1995)CrossRefMATHMathSciNet
296.
van Overschee, P., De Moor, B.: Subspace Identification for Linear Systems. Kluwer Academic, Boston (1996)CrossRefMATH
297.
Verhaegen, M.: Identification of the deterministic part of MIMO state space models given in innovations form from input-output data. Automatica 30, 61–74 (1994)CrossRefMATHMathSciNet
Metadata
Title
Stochastic Systems with Inputs
Authors
Anders Lindquist
Giorgio Picci
Copyright Year
2015
Publisher
Springer Berlin Heidelberg
Book
Linear Stochastic Systems

Print ISBN: 978-3-662-45749-8

Electronic ISBN: 978-3-662-45750-4

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-662-45750-4_17