This study aims to determine how to deal with the identification from input and output data of switched linear systems (SLSs) with Box and Jenkins models. The identification difficulties of this system are that there exist unknown switched signal, unknown middle variables, and colored noise terms in the identification process. To address these issues, the proposed identification method proceeds in two stages, including the estimation of the switched signal of SLSs and the identification of the parameters of all subsystems. First, the Gaussian mixture model is established to represent the distribution of the input and output data of SLSs. Then, the posterior probability is calculated by the expectation-maximization (EM) algorithm and the naive Bayes classifier, and the switched signal is estimated according to the maximum probability criterion. Next, the auxiliary model based multi-innovation generalized extended least square (AM-MI-GELS) algorithm is used to estimate the parameters of all subsystems. Finally, the effectiveness of the proposed method is verified through the simulation example.
AbdelhakGMathieuPEricP, et al. (2016) Convergence analysis of a real-time identification algorithm for switched linear systems with bounded noise. In: 2016 IEEE 55th Conference on Decision and Control (CDC), Las Vegas, NV, 12–14 December 2016, pp. 2957–2962. IEEE.
2.
AbdelhakGMathieuPEricP, et al. (2017) Recursive output error identification algorithm for switched linear systems with bounded noise. IFAC Papersonline50(1): 14112–14117.
3.
AhmadiMMojallaliHWisniewskiR (2017) On robust stability of switched systems in the context of Filippov solutions. Systems and Control Letters109: 17–23.
4.
BakoL (2011) Identification of switched linear systems via sparse optimization. Automatica47(4): 668–677.
5.
BakoLBoukharoubaKDuviellaE, et al. (2011) A recursive identification algorithm for switched linear/affine models. Nonlinear Analysis-Hybrid Systems5(2): 242–253.
6.
BakoLMercèreGLecœucheS (2009) Online structured subspace identification with application to switched linear systems. International Journal of Control82(8): 1496–1515.
7.
BaleghiNAShafieiMH (2016) Stability analysis for discrete-time switched systems with uncertain time delay and affine parametric uncertainties. Transactions of the Institute of Measurement and Control40(4): 1150–1157.
8.
BemporadAGarulliAPaolettiS, et al. (2005) A bounded-error approach to piecewise affine system identification. IEEE Transactions on Automatic Control50(10): 1567–1580.
9.
BorgesJVerdultVVerhaegenM, et al. (2005) A switching detection method based on projected subspace classification. In: Proceedings of the 44th IEEE Conference on Decision and Control, Seville, Spain, 15 December 2005, pp. 344–349. IEEE.
10.
DanielL (2003) Switching in Systems and Control. Boston: Birkhäuser Boston.
11.
KunduAChatterjeeD (2016) A graph theoretic approach to input-to-state stability of switched systems. European Journal of Control29: 44–50.
12.
LauerFBlochGVidalR (2011) A continuous optimization framework for hybrid system identification. Automatica47(3): 608–613.
13.
OnderT (2016) Design and comparison base analysis of adaptive estimator for completely unknown linear systems in the presence of OE noise and constant input time delay. Asian Journal of Control18(3): 1020–1029.
14.
OzayNLagoaCSznaierM (2015) Set membership identification of switched linear systems with known number of subsystems. Automatica51(1): 180–191.
15.
PekpeKMMourotGGassoK, et al. (2004) Identification of switching systems using change detection technique in the subspace framework. In: 2004 43rd IEEE Conference on Decision and Control (CDC), Nassau, 14–17 December 2004, pp. 3720–3725. IEEE.
16.
SaxénJESaxénHToivonenHT (2016) Identification of switching linear systems using self-organizing models with application to silicon prediction in hot metal. Applied Soft Computing47: 271–280.
17.
SefidmazgiMGKordmahallehMMHomaifarA, et al. (2015) Switched linear system identification based on bounded-sitching clustering. In: 2015 American Control Conference (ACC), Chicago, IL, 1–3 July 2015, pp. 1806–1811. IEEE.
18.
SunHLDuanDD (2019) Anti-jamming fault-tolerant control of multi-interference switching systems. System Science and Mathematics37(9): 893–1903.
19.
SunXMWangW (2012) Integral input-to-state stability for hybrid delayed systems with unstable continuous dynamics. Automatica48(9): 2359–2346.
20.
SunZGeS (2005) Analysis and synthesis of switched linear control systems. Automatica41(2): 181–195.
21.
VerdultVVerhaegenM (2004) Subspace identification of piecewise linear systems. In: 2004 43rd IEEE Conference on Decision and Control (CDC), Nassau, 14–17 December 2004, pp. 3838–3843. IEEE.
22.
VidalR (2008) Recursive identification of switched ARX systems. Automatica44(9): 2274–2287.
23.
VidalRSoattoSMaYSastryS (2004) An algebraic geometric approach to the identification of a class of linear hybrid systems. Proceedings of the IEEE Conference on Decision & Control1(1): 167–172.
24.
WangHWXiaH (2019) Identification algorithm of switched systems based on generalized auxiliary model. Journal of Systems Engineering and Electronics30(6): 1224–1232.
25.
WangJChenT (2011) Online identification of switched linear output error models. In: 2011 IEEE International Symposium on Computer-Aided Control System Design (CACSD), Denver, CO, 28–30 September 2011, pp. 1379–1384. IEEE.
26.
ZhangLZhuangSShiP (2015) Non-weighted quasi-time-dependent filtering for switched linear systems with persistent dwell-time. Automatica54: 201–209.
27.
ZhaoJHillD (2008) On stability, L2-gain and control for switched systems. Automatica44(5): 1220–1232.
28.
ZongGWangQYangY (2016) Robustly resilient memory control for time-delay switched systems under asynchronous switching. Transactions of the Institute of Measurement and Control39(9): 1355–1364.
