Identification of fuzzy model of non-uniformly sampled nonlinear systems based on singular value decomposition

WANG Hong-wei1,2 XIE Li-rong1

(1.School of Electrical Engineering, Xinjiang University, Urumqi 830036)
(2.School of Control Science and Control Engineering, Dalian University of Technology, Dalian 116024)

【Abstract】A modeling method based on matrix singular value decomposition (SVD) for model structure identification and parameter estimation is proposed for the nonlinear systems of complex, uncertain, and non-uniformly sampled data. Firstly, the matrix singular value decomposition method is used to analyze the relationship between the local model and the accumulation contribution rates, and the rule number of the fuzzy model is determined. Thus, the structure optimization of the model is realized. Then, in order to overcome the error accumulation and transfer of recursive least squares, this paper adopts the conclusion parameters of the recursive least squares estimation algorithm with singular value decomposition. Finally, a simulation example is given to illustrate the effectiveness of the proposed algorithm.

【Keywords】 nonuniformly sampled system; fuzzy model; singular value decomposition; recursive least squares; structure identification;


【Funds】 National Natural Science Foundation of China (61863034, 51667021) International S&T Cooperation Program of China (2013DFG61520) Science and Technology Aid Project in Xinjiang (2018E02072)

Download this article


    [1] Li X L, Zhou L C, Ding R. Least-squares-based iterative identification algorithm for Hammerstein nonlinear systems with non-uniform sampling [J]. International Journal of Computer Mathematics, 2013, 90 (7):1524–1534.

    [2] Li X L, Zhou L, Ding R F, et al. Recursive least squares estimation algorithm for Hammerstein nonlinear systems with non-uniform sampling [J]. Mathematical Problems in Engineering, 2013, 67 (9): 1811–1818.

    [3] Liu Ranran, Li Haoran, Pan Tianhong, et al. Parameter estimation for non-uniformly sampled wiener systems with dead-zone non-linearities [J]. IFAC-Papers On-Line, 2015, 28 (8): 789–794.

    [4] Zheng Enxing, Liu Ranran, JiangYifeng, et al. Stochastic gradient identification for Hammerstein systems with non-uniformly sampling [J]. Computer Systems Science and Engineering, 2016, 31 (6): 439–444.

    [5] Zhou Lincheng, Li Xiangli, Pan Feng. Gradient-based iterative identification for Wiener nonlinear systems with non-uniform sampling [J]. Nonlinear Dynamics, 2014, 76 (1): 627–634.

    [6] Liu R R, Pan T H, Li Z M. Hierarchical stochastic gradient identification algorithm for non-uniformly sampled Hammerstein-Wiener systems [J]. Control and Decision, 2015, 30 (8): 1491–1496 (in Chinese).

    [7] Xie Li, Yang Huizhong, Ding Feng. Identification of non-uniformly sampled-data systems with asynchronous input and output data [J]. Journal of the Franklin Institute, 2017, 354 (5): 1974–1991.

    [8] Zhou Lincheng, Li Xiangli, Shan Lijie, et al. Hierarchical recursive least squares parameter estimation of non-uniformly sampled Hammerstein nonlinear systems based on Kalman filter [J]. Journal of the Franklin Institute, 2017, 354 (10): 4231–4246.

    [9] Liu Ranran, Pan Tianhong, Li Zhengming. Multi-model recursive identification for nonlinear systems with non-uniformly sampling [J]. Cluster Computer, 2017,13 (1): 25–32.

    [10] Wang H W, Xia H. Fuzzy identification for non-uniformly multi-rate sampled nonlinear systems [J]. Control and Decision, 2015, 30 (9): 1646–1652 (in Chinese).

    [11] Wang HW, Xia H. Fuzzy identification of non-uniformly multirate sampled nonlinear systems based on competitive learning [J]. Journal of Harbin University ofTechnology, 2016, 48 (4): 109–113 (in Chinese).

    [12] Yu X D, Lei Y J, Song Y F, et al. Intuitionistic-fuzzy c-means clustering algorithm based on kernel distance [J]. Journal of Electronics, 2016, 44 (10):2530–2534 (in Chinese).

    [13] LiW, Shah S L, Xiao D. Kalman filters in non-uniformly sampled multirate systems: For FDI and beyond [J]. Automatica, 2008, 44 (1): 199–208.

    [14] Liu Y J, Ding F. Hierarchical least squared identification method for non-uniform periodic sampled system [J]. Control and Decision, 2011, 26 (3): 453–456 (in Chinese).

    [15] Asein N Venkat, Vijaysai P, Ravindra D Gudi. Identification of complex nonlinear processes based on fuzzy decomposition of the steady state space [J]. Journal of Process Control, 2003, 13 (2): 473–488.

This Article


CN: 21-1124/TP

Vol 35, No. 03, Pages 757-762

March 2020


Article Outline


  • 0 Introduction
  • 1 Description of the fuzzy model
  • 2 Optimization of the antecedent structure of fuzzy model based on SVD
  • 3 Recursive identification parameters based on SVD
  • 4 Simulation example
  • 5 Conclusion
  • References