Subspace-based identification of discrete time-delay system

Qiang LIU; Jia-chen MA

doi:10.1631/FITEE.1500358

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Subspace-based identification of discrete time-delay system

Regular Papers | Updated：2022-05-19

- Subspace-based identification of discrete time-delay system
- 基于子空间的离散时滞系统辨识
- Frontiers of Information Technology & Electronic Engineering Vol. 17, Issue 6, Pages: 566-575(2016)
- Affiliations：
  
  1School of Astronautics, Harbin Institute of Technology, Harbin 150001, China
  2School of Information and Electrical Engineering, Harbin Institute of Technology, Weihai 264209, China
- Author bio：
  
  E-mail:lqianghit@163.com
- Funds：
- DOI：10.1631/FITEE.1500358
  CLC： TP242.6
- Received：23 October 2015，
  
  Accepted：14 March 2016，
  
  Published：2016-06
- Accepted：
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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.
DOI：

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. DOI： 10.1631/FITEE.1500358.

摘要

目的

时滞存在于很多系统中，时滞会导致系统性能下降并使系统变得不稳定。因此研究具有未知时滞的线性辨识对于系统分析和控制设计有着很重要的作用。本文提出了一种ACS算法，用来解决具有单一时延的离散随机时滞系统的辨识。

创新点

提出一种ACS算法，将时滞系统矩阵从估计的增广矩阵中重新恢复出来。采用状态增广方法将时滞系统与等价的线性时不变系统联系起来，利用N4SID算法对增广系统矩阵进行初始估计。

方法

时滞系统被表达为具有单一时延的时滞差分方程。首先利用状态增广方法将线性时滞系统转化为一个等价的线性时不变系统。然后利用子空间辨识方法对增广系统矩阵进行初始估计，提出了一种ACS算法，得到了线性时滞系统的状态空间模型。最后通过解决两个最小二乘法问题，利用卡尔曼状态序列和输入输出数据得到相同状态空间下的时滞系统矩阵。

结论

本文提出的ACS算法可以利用估计的增广矩阵得出时滞系统矩阵，解决了线性离散时滞系统的辨识问题，同时证明了该算法具有良好的局部收敛性能。仿真结果表明了这种算法的有效性。

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.

关键词

Keywords

references

A Bayrak , , , E Tatlicioglu . . A novel online adaptive time delay identification technique . . Int. J. Syst. Sci. , , 2016 . . 47 ( ( 7 ): ): 1574 - - 1585 . . DOI: 10.1080/00207721.2014.941958 http://doi.org/10.1080/00207721.2014.941958 . .

L Belkoura , , , Y Orlov . . Identifiability analysis of linear delay-differential systems . . IMA J. Math. Contr. Inform. , , 2002 . . 19 ( ( 1-2 ): ): 73 - - 81 . . DOI: 10.1093/imamci/19.1_and_2.73 http://doi.org/10.1093/imamci/19.1_and_2.73 . .

SX Ding , , , P Zhang , , , A Naik , , , 等 . . Subspace method aided data-driven design of fault detection and isolation systems . . J. Process Contr. , , 2009 . . 19 ( ( 9 ): ): 1496 - - 1510 . . DOI: 10.1016/j.jprocont.2009.07.005 http://doi.org/10.1016/j.jprocont.2009.07.005 . .

SV Drakunov , , , W Perruquetti , , , JP Richard , , , 等 . . Delay identification in time-delay systems using variable structure observers . . Ann. Rev. Contr. , , 2006 . . 30 ( ( 2 ): ): 143 - - 158 . . DOI: 10.1016/j.arcontrol.2006.08.001 http://doi.org/10.1016/j.arcontrol.2006.08.001 . .

H Gao , , , T Chen . . New results on stability of discrete-time systems with time-varying state delay . . IEEE Trans. Autom. Contr. , , 2007 . . 52 ( ( 2 ): ): 328 - - 334 . . DOI: 10.1109/TAC.2006.890320 http://doi.org/10.1109/TAC.2006.890320 . .

J Gorski , , , F Pfeuffer , , , K Klamroth . . Biconvex sets and optimization with biconvex functions: a survey and ex-tensions . . Math. Methods Oper. Res. , , 2007 . . 66 ( ( 3 ): ): 373 - - 407 . . DOI: 10.1007/s00186-007-0161-1 http://doi.org/10.1007/s00186-007-0161-1 . .

S Hachicha , , , M Kharrat , , , A Chaari . . N4SID and MOESP algorithms to highlight the ill-conditioning into subspace identification . . Int. J. Autom. Comput. , , 2014 . . 11 ( ( 1 ): ): 30 - - 38 . . DOI: 10.1007/s11633-014-0763-z http://doi.org/10.1007/s11633-014-0763-z . .

B Huang , , , R Kadali . . Dynamic Modeling, Predictive Control and Performance Monitoring: a Data-Driven Subspace Approach , , 2008 . . : London, UK : Springer , , DOI: 10.1007/978-1-84800-233-3 http://doi.org/10.1007/978-1-84800-233-3 . .

B Huang , , , SX Ding , , , SJ Qin . . Closed-loop subspace identification: an orthogonal projection approach . . J. Process Contr. , , 2005 . . 15 ( ( 1 ): ): 53 - - 66 . . DOI: 10.1016/j.jprocont.2004.04.007 http://doi.org/10.1016/j.jprocont.2004.04.007 . .

T Kailath . . Linear Systems , , 1980 . . : New Jersey, USA : Prentice-Hall , , . .

V Kolmanovskii , , , A Myshkis . . Introduction to the Theory and Applications of Functional Differential Equations , , 1999 . . : Springer : the Netherlands , , DOI: 10.1007/978-94-017-1965-0 http://doi.org/10.1007/978-94-017-1965-0 . .

P Kudva , , , KS Narendra . . An Identification Procedure for Discrete Multivariable Systems . . Technical Report No. AD0768992, Yale University, USA , , 1973 . . .

RBC Lima , , , PR Barros . . Identification of time-delay systems: a state-space realization approach . . Proc. 9th IFAC Symp. on Advanced Control of Chemical Processes , , 2015 . . 254 - - 259 . . DOI: 10.1016/j.ifacol.2015.08.190 http://doi.org/10.1016/j.ifacol.2015.08.190 . .

L Ljung . . System Identification: Theory for the User , , 1987 . . : New Jersey, USA : PTR Prentice Hall , , . .

SMV Lunel . . Parameter identifiability of differential delay equations . . Int. J. Adapt. Contr. Signal Process. , , 2001 . . 15 ( ( 6 ): ): 655 - - 678 . . DOI: 10.1002/acs.690 http://doi.org/10.1002/acs.690 . .

C Lyzell , , , M Enqvist , , , L Ljung , , , 等 . . Handling Certain Structure Information in Subspace Identification . . 2009 . . Report, Linkping University Electronic Press, Sweden. . . . .

S Nakagiri , , , M Yamamoto . . Unique identification of coefficient matrices, time delays and initial functions of functional differential equations . . J. Math. Syst. Estimat. Contr. , , 1995 . . 5 ( ( 3 ): ): 323 - - 344 . . . .

SI Niculescu . . Delay Effects on Stability: a Robust Control Approach , , 2001 . . : London, UK : Springer-Verlag , , DOI: 10.1007/1-84628-553-4 http://doi.org/10.1007/1-84628-553-4 . .

Y Orlov , , , L Belkoura , , , JP Richard , , , 等 . . On identi-fiability of linear time-delay systems . . IEEE Trans. Autom. Contr. , , 2002 . . 47 ( ( 8 ): ): 1319 - - 1324 . . DOI: 10.1109/TAC.2002.801202 http://doi.org/10.1109/TAC.2002.801202 . .

Y Orlov , , , L Belkoura , , , JP Richard , , , 等 . . Adaptive identification of linear time-delay systems . . Int. J. Robust Nonl. Contr. , , 2003 . . 13 ( ( 9 ): ): 857 - - 872 . . DOI: 10.1002/rnc.850 http://doi.org/10.1002/rnc.850 . .

JH Park , , , S Han , , , B Kwon . . On-line model parameter estimations for time-delay systems . . IEICE Trans. Inform. Syst. , , 2013 . . 96 ( ( 8 ): ): 1867 - - 1870 . . . .

F Pourboghrat , , , DH Chyung . . Parameter identification of linear delay systems . . Int. J. Contr. , , 1989 . . 49 ( ( 2 ): ): 595 - - 627 . . DOI: 10.1080/00207178908559656 http://doi.org/10.1080/00207178908559656 . .

O Prot , , , G Mercère . . Initialization of gradient-based optimization algorithms for the identification of structured state-space models . . Proc. 18th IFAC World Congress , , 2011 . . 10782 - - 10787 . . . .

P Qin , , , S Kanae , , , ZJ Yang , , , 等 . . Identification of lifted models for general dual-rate sampled-data systems based on input-output data . . 2007 . . Proc. Asian Modelling and Simulation . . 1 - - 12 . . . .

SJ Qin . . An overview of subspace identification . . Comput. Chem. Eng. , , 2006 . . 30 ( ( 10-12 ): ): 1502 - - 1513 . . DOI: 10.1016/j.compchemeng.2006.05.045 http://doi.org/10.1016/j.compchemeng.2006.05.045 . .

JP Richard . . Time-delay systems: an overview of some recent advances and open problems . . Automatica , , 2003 . . 39 ( ( 10 ): ): 1667 - - 1694 . . DOI: 10.1016/S0005-1098(03)00167-5 http://doi.org/10.1016/S0005-1098(03)00167-5 . .

J Wang , , , SJ Qin . . Closed-loop subspace identification using the parity space . . Automatica , , 2006 . . 42 ( ( 2 ): ): 315 - - 320 . . DOI: 10.1016/j.automatica.2005.09.012 http://doi.org/10.1016/j.automatica.2005.09.012 . .

L Xie , , , L Ljung . . Estimate physical parameters by black box modeling . . Proc. 21st Chinese Control Conf. , , 2002 . . 673 - - 677 . . . .

X Yang , , , H Gao . . Multiple model approach to linear parameter varying time-delay system identification with EM algorithm . . J. Franklin Inst. , , 2014 . . 351 ( ( 12 ): ): 5565 - - 5581 . . DOI: 10.1016/j.jfranklin.2014.09.015 http://doi.org/10.1016/j.jfranklin.2014.09.015 . .

X Yang , , , Y Lu , , , Z Yan . . Robust global identification of linear parameter varying systems with generalised expectation-maximisation algorithm . . IET Contr. Theory Appl. , , 2015 . . 9 ( ( 7 ): ): 1103 - - 1110 . . DOI: 10.1049/iet-cta.2014.0694 http://doi.org/10.1049/iet-cta.2014.0694 . .

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