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In order to be able to identify the hyper-chaotic l system with uncertain parameters effectively in real time, so that hyper-chaotic system control and synchronization tracking can be applied, this paper presents a system identification method for the hyper-chaotic system based on Wiener model. The linear part of the Wiener model consists of linear transversal filters, while the nonlinear part is represented approximately by piecewise linear filters. According to the minimum mean square error criterion, the filter parameter updated algorithm is derived, and the convergence condition is also obtained. Simulation results confirm the effectiveness of the adaptive filter for the identification of hyper-chaotic systems. The presented method not only overcomes the difficulty to identify a strongly nonlinear system only by adaptive linear filters, but also have a lower computational complexity compared with other non-linear adaptive filters.
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Keywords:
- Wiener model /
- adaptive identification /
- hyper-chaotic system /
- PWL filter
[1] Wills A, Schn T B, Ljung L, Ninness B 2013 Automatica 49 70
[2] Shafiee G, Arefi M M, Jahed-Motlagh M R, Jalali A A 2008 Chem. Eng. J. 143 282
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[15] [16] Huang L L, Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese)[黄丽莲, 齐雪 2013 62 080507]
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[19] [20] [21] Yang D S, Liu Z W, Zhao Y, Liu Z B 2012 Chin. Phys. B 21 040503
[22] [23] Xu Y H, Li B, Zhou W N, Fang J A 2012 Nonlinear. Dynam. 70 289
[24] [25] Luo R Z, Wang Y L 2012 Chaos. 22 023109
[26] [27] Li D, Deng L M, Du Y X, Yang Y 2012 Acta Phys. Sin. 61 050502 (in Chinese)[李东, 邓良明, 杜永霞, 杨媛 2012 61 050502]
[28] [29] Zhang H L, Song L L 2013 Acta Phys. Sin. 62 190508 (in Chinese)[张宏立, 宋莉莉 2013 62 190508]
[30] [31] Zhu D R, Liu C X, Yan B N 2012 Chin. Phys. B 21 090509
[32] Gu W D, Sun Z Y, Wu X M, Yu C B 2013 Chin. Phys. B 22 090203
[33] [34] Haykin S 2002 Adaptive filter theory (New York: Pearson Education)
[35] [36] Zheng C D, Shan Q H, Zhang H G, Wang Z S 2013 IEEE Trans. Neural. Networks. Learning. Syst. 24 800
[37] [38] [39] Chen A M, Junan Lu J N, L J H, Yu S M 2006 Phys. A 364 103
[40] Chua L O, Deng A C 1988 IEEE Trans. Circ. Syst. 35 101
[41] [42] [43] Julian P 1999 High level canonical piecewise linear representation: Theory and applications. (Ph. D. thesis in Systems Control, Universidad Nacional del Sur, UMI Dissertation Services)
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[1] Wills A, Schn T B, Ljung L, Ninness B 2013 Automatica 49 70
[2] Shafiee G, Arefi M M, Jahed-Motlagh M R, Jalali A A 2008 Chem. Eng. J. 143 282
[3] [4] Peng J Z, Dubay R 2011 ISA Trans 50 588
[5] [6] Silvina I B, Jos L F 2011 Comput. Chem. Eng. 35 2867
[7] [8] Zhao Z J, Zheng X H, Shen L 2010 J. Circ. Syst. 15 11 (in Chinese) [赵知劲, 郑晓华, 沈雷 2010 电路与系统学报 15 11]
[9] [10] Figueroa J L, Cousseau J E, Figueiredo R J P de 2004 Circ. Syst. Signal. Proc. 23 365
[11] [12] Liu X F, Yang X Q, Zheng N N 2012 Neurocomputing 79 132
[13] [14] Ma T D, Jiang W B, Fu J, Chai Y 2012 Acta Phys. Sin. 61 160506 (in Chinese)[马铁东, 江伟波, 浮洁, 柴毅 2012 61 160506]
[15] [16] Huang L L, Qi X 2013 Acta Phys. Sin. 62 080507 (in Chinese)[黄丽莲, 齐雪 2013 62 080507]
[17] [18] Yang J, Sun Q Y, Yang D S 2012 Acta Phys. Sin. 61 200511 (in Chinese)[杨珺, 孙秋野, 杨东升 2012 61 200511]
[19] [20] [21] Yang D S, Liu Z W, Zhao Y, Liu Z B 2012 Chin. Phys. B 21 040503
[22] [23] Xu Y H, Li B, Zhou W N, Fang J A 2012 Nonlinear. Dynam. 70 289
[24] [25] Luo R Z, Wang Y L 2012 Chaos. 22 023109
[26] [27] Li D, Deng L M, Du Y X, Yang Y 2012 Acta Phys. Sin. 61 050502 (in Chinese)[李东, 邓良明, 杜永霞, 杨媛 2012 61 050502]
[28] [29] Zhang H L, Song L L 2013 Acta Phys. Sin. 62 190508 (in Chinese)[张宏立, 宋莉莉 2013 62 190508]
[30] [31] Zhu D R, Liu C X, Yan B N 2012 Chin. Phys. B 21 090509
[32] Gu W D, Sun Z Y, Wu X M, Yu C B 2013 Chin. Phys. B 22 090203
[33] [34] Haykin S 2002 Adaptive filter theory (New York: Pearson Education)
[35] [36] Zheng C D, Shan Q H, Zhang H G, Wang Z S 2013 IEEE Trans. Neural. Networks. Learning. Syst. 24 800
[37] [38] [39] Chen A M, Junan Lu J N, L J H, Yu S M 2006 Phys. A 364 103
[40] Chua L O, Deng A C 1988 IEEE Trans. Circ. Syst. 35 101
[41] [42] [43] Julian P 1999 High level canonical piecewise linear representation: Theory and applications. (Ph. D. thesis in Systems Control, Universidad Nacional del Sur, UMI Dissertation Services)
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