Identification of continuous-time state-space models from non-uniform fast-sampled data
Identification of continuous-time state-space models from non-uniform fast-sampled data
- Author(s): J.I. Yuz ; J. Alfaro ; J.C. Agüero ; G.C. Goodwin
- DOI: 10.1049/iet-cta.2010.0246
For access to this article, please select a purchase option:
Buy article PDF
Buy Knowledge Pack
IET members benefit from discounts to all IET publications and free access to E&T Magazine. If you are an IET member, log in to your account and the discounts will automatically be applied.
Thank you
Your recommendation has been sent to your librarian.
- Author(s): J.I. Yuz 1 ; J. Alfaro 1 ; J.C. Agüero 2 ; G.C. Goodwin 2
-
-
View affiliations
-
Affiliations:
1: Electronic Engineering Department, Universidad Técnica Federico Santa María (UTFSM), Valparaíso, Chile
2: Centre for Complex Dynamics Systems and Control (CDSC), University of Newcastle, Australia
-
Affiliations:
1: Electronic Engineering Department, Universidad Técnica Federico Santa María (UTFSM), Valparaíso, Chile
- Source:
Volume 5, Issue 7,
5 May 2011,
p.
842 – 855
DOI: 10.1049/iet-cta.2010.0246 , Print ISSN 1751-8644, Online ISSN 1751-8652
In this study, we apply the expectation-maximisation (EM) algorithm to identify continuous-time state-space models from non-uniformly fast-sampled data. The sampling intervals are assumed to be small and uniformly bounded. The authors use a parameterisation of the sampled-data model in incremental form in order to modify the standard formulation of the EM algorithm for discrete-time models. The parameters of the incremental model converge to the parameter of the continuous-time system description as the sampling period goes to zero. The benefits of the proposed algorithm are successfully demonstrated via simulation studies.
Inspec keywords: state-space methods; expectation-maximisation algorithm; discrete time systems
Other keywords:
Subjects: Discrete control systems; Interpolation and function approximation (numerical analysis)
References
-
-
1)
- J. Durbin , S.J. Koopman . (2005) Time series analysis by state space methods.
-
2)
- H. Rauch , F. Tung , C. Striebel . Maximum likelihood estimates of linear dynamic systems. AIAA J. , 8 , 1445 - 1450
-
3)
- F. Ding , L. Qiu , T. Chen . Reconstruction of continuous-time systems from their non-uniformly sampled discrete-time systems. Automatica , 2 , 324 - 332
-
4)
- B. Øksendal . (2003) Stochastic differential equations: an introduction with applications.
-
5)
- M.J. Newman , D.G. Holmes . Delta operator digital filters for high performance inverter applications. IEEE Trans. Power Electron. , 1 , 447 - 454
-
6)
- M. Mansour . (1993) Stability and robust stability of discrete-time systems in the δ-transform, Fundamentals of discrete-time systems: a tribute to Prof. Eliahu I. Jury.
-
7)
- Agüero, J.C., Yuz, J.I., Goodwin, G.C.: `Frequency domain identification of MIMO state space models using the EM algorithm', European Control Conf. – ECC’07, 2007, Kos, Greece.
-
8)
- S. Chirarattananon , B. Anderson . The fixed-lag smoother as a stable finite-dimensional linear system. Automatica , 6 , 657 - 669
-
9)
- G.C. Goodwin , S. Graebe , M.E. Salgado . (2001) Control system design.
-
10)
- McKelvey, T., Helmersson, A.: `State space parameterization of multivariable linear systems using tridiagonal matrix form', 35thIEEE Conf. on Decision and Control, 1996.
-
11)
- A. Feuer , G.C. Goodwin . (1996) Sampling in digital signal processing and control.
-
12)
- J. Gillberg , L. Ljung . Frequency domain identification of continuous-time output error models, part II: non-uniformly sampled data and B-spline output approximation. Automatica , 1 , 11 - 18
-
13)
- A.P. Dempster , N.M. Laird , D.B. Rubin . Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. B , 1 , 1 - 38
-
14)
- K. Premaratne , E.I. Jury . Tabular method for determining root distribution of delta-operator formulated real polynomials. IEEE Trans. Autom. Control , 2 , 352 - 355
-
15)
- R.H. Shumway , D.S. Stoffer . An approach to time series smoothing and forecasting using the EM algorithm. J. Time Ser. Anal. , 253 - 264
-
16)
- R. Pintelon , J. Schoukens . (2001) System identification: a frequency domain approach.
-
17)
- P. Suchomski . Numerically robust delta-domain solutions to discrete-time Lyapunov equations. Syst. Control Lett. , 4 , 319 - 326
-
18)
- T. Kailath , P. Frost . An innovations approach to least-squares estimation – part II: linear smoothing in additive white noise. IEEE Trans, Autom. Control , 6 , 655 - 660
-
19)
- R. Shumway , D. Stoffer . (2006) Time series analysis and its applications.
-
20)
- M.E. Salgado , R.H. Middleton , G.C. Goodwin . Connection between continuous and discrete Riccati equations with applications to Kalman filtering. IEE Proc. Control Theory Appl. , 1 , 28 - 34
-
21)
- K. Premaratne , S. Touset , E.I. Jury . Root distribution of delta-operator formulated polynomials. IEE Proc. Control Theory Appl. , 1 , 1 - 12
-
22)
- G.C. Goodwin , R.L. Payne . (1977) Dynamic system identification: experiment design and data analysis.
-
23)
- M. Deistler , G.C. Goodwin . (2000) System identification-general aspects and structure, Model identification and adaptive control: from windsurfing to telecommunications.
-
24)
- P.E. Kloeden , E. Platen . (1992) Numerical solution of stochastic differential equations.
-
25)
- Agüero, J.C., Yuz, J.I., Goodwin, G.C., Tang, W.: `Identification of state-space systems using a dual time-frequency domain approach', 49thIEEE Conf. on Decision and Control, 2010.
-
26)
- V. Kadirkamanathan , S. Anderson . Maximum-likelihood estimation of delta-domain model parameters from noisy output signals. IEEE Trans. Signal Process. , 3765 - 3770
-
27)
- K. Aström . (1970) Introduction to stochastic control theory.
-
28)
- C.F.J. Wu . On the convergence properties of the EM algorithm. Ann. Stat. , 1 , 95 - 103
-
29)
- S. Gibson , B. Ninness . Robust maximum-likelihood estimation of multivariables dynamic systems. Automatica , 10 , 1667 - 1682
-
30)
- A. Wills , B. Ninnesss , S. Gibson . Maximum likelihood estimation of state space models from frequency domain data. IEEE Trans. Autom. Control , 1 , 19 - 33
-
31)
- E.J. Hannan . The identification and parameterization of ARMAX and state space forms. Econometrica , 4 , 713 - 723
-
32)
- E. Larsson , T. Söderström . Identification of continuous-time AR processes from unevenly sampled data. Automatica , 709 - 718
-
33)
- A.H. Jazwinski . (1970) Stochastic processes and filtering theory.
-
34)
- G.C. Goodwin , J.I. Yuz , M.E. Salgado , J.C. Agüero . Variance or spectral density in sampled data filtering?. J. Glob. Optim. (to appear)
-
35)
- G.C. Goodwin , R.H. Middleton , H.V. Poor . High-speed digital signal processing and control. Proc. IEEE , 2 , 240 - 259
-
36)
- G.C. Goodwin , A. Feuer . Estimation with missing data. Math. Comput. Model. Dyn. Syst. , 3 , 220 - 244
-
37)
- J. Meditch . A survey of data smoothing for linear and nonlinear dynamic systems. Automatica , 2 , 151 - 162
-
38)
- A. Bryson , Y. Ho . (1975) Applied optimal control: optimization, estimation, and control.
-
39)
- R.H. Middleton , G.C. Goodwin . (1990) Digital control and estimation: a unified approach.
-
40)
- L. Ljung , A. Wills . Issues in sampling and estimating continuous-time models with stochastic disturbances. Automatica , 5 , 925 - 931
-
41)
- A. Isaksson . Identification of ARX models subject to missing data. IEEE Trans. Autom. Control , 5 , 813 - 819
-
1)