CLC number: TP242.6
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2016-05-06
Cited: 0
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Qiang Liu, Jia-chen Ma. Subspace-based identification of discrete time-delay system[J]. Frontiers of Information Technology & Electronic Engineering, 2016, 17(6): 566-575.
@article{title="Subspace-based identification of discrete time-delay system",
author="Qiang Liu, Jia-chen Ma",
journal="Frontiers of Information Technology & Electronic Engineering",
volume="17",
number="6",
pages="566-575",
year="2016",
publisher="Zhejiang University Press & Springer",
doi="10.1631/FITEE.1500358"
}
%0 Journal Article
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%A Jia-chen Ma
%J Frontiers of Information Technology & Electronic Engineering
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%I Zhejiang University Press & Springer
%DOI 10.1631/FITEE.1500358
TY - JOUR
T1 - Subspace-based identification of discrete time-delay system
A1 - Qiang Liu
A1 - Jia-chen Ma
J0 - Frontiers of Information Technology & Electronic Engineering
VL - 17
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SP - 566
EP - 575
%@ 2095-9184
Y1 - 2016
PB - Zhejiang University Press & Springer
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DOI - 10.1631/FITEE.1500358
Abstract: We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant (LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search (ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.
This paper is concerned with the identification problems for a class of linear stochastic time-delay systems with unknown delayed states. The time-delay system is expressed as a delay differential equation with a single delay in state vector and conventional subspace identification method is utilized to estimate the augmented system matrices. The time-delay system matrices, under the same state space basis, are recovered from the Kalman state sequences and input-output data. Finally, authors validated their theoretical results by providing numerical examples.
[1]Bayrak, A., Tatlicioglu, E., 2016. A novel online adaptive time delay identification technique. Int. J. Syst. Sci., 47(7):1574-1585.
[2]Belkoura, L., Orlov, Y., 2002. Identifiability analysis of linear delay-differential systems. IMA J. Math. Contr. Inform., 19(1-2):73-81.
[3]Ding, S.X., Zhang, P., Naik, A., et al., 2009. Subspace method aided data-driven design of fault detection and isolation systems. J. Process Contr., 19(9):1496-1510.
[4]Drakunov, S.V., Perruquetti, W., Richard, J.P., et al., 2006. Delay identification in time-delay systems using variable structure observers. Ann. Rev. Contr., 30(2):143-158.
[5]Gao, H., Chen, T., 2007. New results on stability of discrete-time systems with time-varying state delay. IEEE Trans. Autom. Contr., 52(2):328-334.
[6]Gorski, J., Pfeuffer, F., Klamroth, K., 2007. Biconvex sets and optimization with biconvex functions: a survey and extensions. Math. Methods Oper. Res., 66(3):373-407.
[7]Hachicha, S., Kharrat, M., Chaari, A., 2014. N4SID and MOESP algorithms to highlight the ill-conditioning into subspace identification. Int. J. Autom. Comput., 11(1):30-38.
[8]Huang, B., Kadali, R., 2008. Dynamic Modeling, Predictive Control and Performance Monitoring: a Data-Driven Subspace Approach. Springer, London, UK.
[9]Huang, B., Ding, S.X., Qin, S.J., 2005. Closed-loop subspace identification: an orthogonal projection approach. J. Process Contr., 15(1):53-66.
[10]Kailath, T., 1980. Linear Systems. Prentice-Hall, New Jersey, USA.
[11]Kolmanovskii, V., Myshkis, A., 1999. Introduction to the Theory and Applications of Functional Differential Equations. Springer, the Netherlands.
[12]Kudva, P., Narendra, K.S., 1973. An Identification Procedure for Discrete Multivariable Systems. Technical Report No. AD0768992, Yale University, USA.
[13]Lima, R.B.C., Barros, P.R., 2015. Identification of time-delay systems: a state-space realization approach. Proc. 9th IFAC Symp. on Advanced Control of Chemical Processes, p.254-259.
[14]Ljung, L., 1987. System Identification: Theory for the User. PTR Prentice Hall, New Jersey, USA.
[15]Lunel, S.M.V., 2001. Parameter identifiability of differential delay equations. Int. J. Adapt. Contr. Signal Process., 15(6):655-678.
[16]Lyzell, C., Enqvist, M., Ljung, L., 2009. Handling Certain Structure Information in Subspace Identification. Report, Linköping University Electronic Press, Sweden.
[17]Nakagiri, S., Yamamoto, M., 1995. Unique identification of coefficient matrices, time delays and initial functions of functional differential equations. J. Math. Syst. Estimat. Contr., 5(3):323-344.
[18]Niculescu, S.I., 2001. Delay Effects on Stability: a Robust Control Approach. Springer-Verlag, London, UK.
[19]Orlov, Y., Belkoura, L., Richard, J.P., et al., 2002. On identifiability of linear time-delay systems. IEEE Trans. Autom. Contr., 47(8):1319-1324.
[20]Orlov, Y., Belkoura, L., Richard, J.P., et al., 2003. Adaptive identification of linear time-delay systems. Int. J. Robust Nonl. Contr., 13(9):857-872.
[21]Park, J.H., Han, S., Kwon, B., 2013. On-line model parameter estimations for time-delay systems. IEICE Trans. Inform. Syst., 96(8):1867-1870.
[22]Pourboghrat, F., Chyung, D.H., 1989. Parameter identification of linear delay systems. Int. J. Contr., 49(2):595-627.
[23]Prot, O., Mercère, G., 2011. Initialization of gradient-based optimization algorithms for the identification of structured state-space models. Proc. 18th IFAC World Congress, p.10782-10787.
[24]Qin, P., Kanae, S., Yang, Z.J., et al., 2007. Identification of lifted models for general dual-rate sampled-data systems based on input-output data. Proc. Asian Modelling and Simulation, p.7-12.
[25]Qin, S.J., 2006. An overview of subspace identification. Comput. Chem. Eng., 30(10-12):1502-1513.
[26]Richard, J.P., 2003. Time-delay systems: an overview of some recent advances and open problems. Automatica, 39(10):1667-1694.
[27]Wang, J., Qin, S.J., 2006. Closed-loop subspace identification using the parity space. Automatica, 42(2):315-320.
[28]Xie, L., Ljung, L., 2002. Estimate physical parameters by black box modeling. Proc. 21st Chinese Control Conf., p.673-677.
[29]Yang, X., Gao, H., 2014. Multiple model approach to linear parameter varying time-delay system identification with EM algorithm. J. Franklin Inst., 351(12):5565-5581.
[30]Yang, X., Lu, Y., Yan, Z., 2015. Robust global identification of linear parameter varying systems with generalised expectation-maximisation algorithm. IET Contr. Theory Appl., 9(7):1103-1110.
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