Document Type : Research Articles


1 University of Sistan and Baluchestan

2 Khorasan Institute of Higher Education


This paper presents a new algorithm for the identification of a specific class of hybrid systems. Hybrid System identification is a challenging problem since it involves the estimation of discrete and continuous states simultaneously. Using the method known as product of errors, this problem could be formulated such that, the identification of continuous state to be independent of discrete state estimation. We propose a new iterative weighted least squares algorithm (IWLS) for the identification of switched auto regressive exogenous systems (SARX). In this method, the parameters of only one subsystem are updated at each iteration while the parameters of the other subsystems are assumed known. In the method, all four main parameters of hybrid systems, namely Subsystem degrees, Number of subsystems, Unknown parameters vector and switching signal are estimated. Simulation results shows that our proposed method has a good performance in identifying the subsystems parameters and switching signal. Also, the superiority of our algorithm is shown by modeling of two SARX systems.


[1] J. Roll, A. Bemporad, and L. Ljung, "Identification of
piecewise affine systems via mixed-integer
programming," Automatica, vol. 40, no. 1, pp. 37-50,

[2] R. Vidal, S. Soatto, Y. Ma, and S. Sastry, "An
algebraic geometric approach to the identification of a
class of linear hybrid systems," in 42nd IEEE
International Conference on Decision and Control
(IEEE Cat. No. 03CH37475), vol. 1: IEEE, pp. 167-
172, 2003.

[3] A. L. Juloski, S. Weiland, and W. Heemels, "A
Bayesian approach to identification of hybrid
systems," IEEE Transactions on Automatic Control,
vol. 50, no. 10, pp. 1520-1533, 2005.

[4] A. Bemporad, A. Garulli, S. Paoletti, and A. Vicino,
"A bounded-error approach to piecewise affine system identification," IEEE Transactions on Automatic
Control, vol. 50, no. 10, pp. 1567-1580, 2005.

[5] M. Petreczky, L. Bako, S. Lecoeuche, and K. Motchon, "Minimality and identifiability of discrete-
time SARX systems," arXiv preprint arXiv:2002.01818, 2020.

[6] S. Hojjatinia, C. M. Lagoa, "Identification of
switched autoregressive exogenous systems from
large noisy datasets," International Journal of Robust
and Nonlinear Control, vol. 30, no. 15, pp. 5777-5801,

[7] Z. Du, L. Balzano, and N. Ozay, "A robust algorithm for online switched system identification," IFAC-
PapersOnLine, vol. 51, no. 15, pp. 293-298, 2018.
[8] Y. Lu, S. Khatibisepehr, and B. Huang, "A variational
Bayesian approach to identification of switched ARX
models," in 53rd IEEE Conference on Decision and
Control,: IEEE, pp. 2542-2547, 2014.

[9] S. Nazari, B. Rashidi, Q. Zhao, and B. Huang, "An
iterative algebraic geometric approach for
identification of switched arx models with noise,"
Asian Journal of Control, vol. 18, no. 5, pp. 1655-
1667, 2016.

[10] P. Mattsson, D. Zachariah, and P. Stoica,
"Recursive identification method for piecewise ARX
models: A sparse estimation approach," IEEE
Transactions on Signal Processing, vol. 64, no. 19, pp.
5082-5093, 2016.

[11] M. Teshnehlab and M. Aliyari-shore-deli, "Fault
detection and identification of high dimensionsystem
by GLOLIMOT," International journal of Industrial
Electronics, Control and Optimization, vol. 2, no. 4,
pp.331 -342, 2019.