Control of fractional order chaotic system based on least square support vector machines

Yan Xiao-Mei; Liu Ding

doi:10.7498/aps.59.3043

Abstract

A new method based on least square support vector machines (LS-SVM) is proposed for chaos control of fractional order system. Based on the stability theory of fractional order linear system, the system is decomposed into stable linear parts and the corresponding nonlinear parts. The active controller is designed to compensate the nonlinear parts by using the excellent nonlinearity approximation ability and better generalization capacity of LS-SVM. Thus fractional order chaotic system is suppressed to the equilibrium point. Fractional order Liu system and fractional order Chen system are illustrated respectively. The simulation results verify the effectiveness and feasibility of the proposed method.

Keywords:

Authors and contacts

1.
西安理工大学自动化与信息工程学院，西安 710048

References

[1]	［1］Bagley R L, Calico R A 1991 J. Guid. Control Dyn. 14 304
[2]	［2］Sun H H, Abdelwahad A A, Onaral B 1984 IEEE Trans.Automat. Control. 29 441
[3]	［3］Ichise M, Nagayanagi Y, Kojima T 1971 J. Electro-Anal.Chem. 33 253
[4]	［4］Li C P, Peng G J 2004 Chaos Soliton. Fract. 22 443
[5]	［5］Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[6]	［6］Ge Z M, Ou C Y 2007 Chaos Soliton. Fract. 34 262
[7]	［7］Lu J G 2006 Phys. Lett. A 354 305
[8]	［8］Liu C X 2007 Acta Phys. Sin. 56 6865 (in Chinese) ［刘崇新 2007 物理学报 56 6865］
[9]	［9］Li C G, Chen G R 2004 Chaos Soliton. Fract. 22 549
[10]	］Gao X, Yu J B 2005 Chin. Phys. 14 908
[11]	］Zhang C F, Gao J F, Xu L 2007 Acta Phys. Sin. 56 5124 (in Chinese) ［张成芬、高金峰、徐磊 2007 物理学报 56 5124］
[12]	］Zhong Q S, Bao J F, Yu Y B, Liao X F 2009 Chin. Phys. Lett. 25 2812
[13]	］Vapnik V N 2000 The nature of statistical learning theory (2nd ed) (New York: Springer-Vedag) p125
[14]	］Suykens J A K, Vandewalle J 1999 Int. J. Circ. Theor. Appl. 27 605
[15]	］Ye M Y 2005 Acta Phys. Sin. 54 30 (in Chinese) ［叶美盈 2005 物理学报 54 30 ］
[16]	］Liu H, Liu D, Ren H P 2005 Acta Phys. Sin. 54 4019 (in Chinese) ［刘涵、刘丁、任海鹏 2005 物理学报 54 4019］
[17]	］Podlubny I 1999 Fractional differential equations (1st ed) (New York: Academic Press) p41
[18]	］Matignon D 1996 IMACS- SMC Proceedings, Lille, France, July, 1996 p963
[19]	］Ahmed E, El-Sayed A M A, El-Saka H A A 2007 J. Math. Anal. Appl. 325 542

Cited By

[1]	［1］Bagley R L, Calico R A 1991 J. Guid. Control Dyn. 14 304
[2]	［2］Sun H H, Abdelwahad A A, Onaral B 1984 IEEE Trans.Automat. Control. 29 441
[3]	［3］Ichise M, Nagayanagi Y, Kojima T 1971 J. Electro-Anal.Chem. 33 253
[4]	［4］Li C P, Peng G J 2004 Chaos Soliton. Fract. 22 443
[5]	［5］Grigorenko I, Grigorenko E 2003 Phys. Rev. Lett. 91 034101
[6]	［6］Ge Z M, Ou C Y 2007 Chaos Soliton. Fract. 34 262
[7]	［7］Lu J G 2006 Phys. Lett. A 354 305
[8]	［8］Liu C X 2007 Acta Phys. Sin. 56 6865 (in Chinese) ［刘崇新 2007 物理学报 56 6865］
[9]	［9］Li C G, Chen G R 2004 Chaos Soliton. Fract. 22 549
[10]	］Gao X, Yu J B 2005 Chin. Phys. 14 908
[11]	］Zhang C F, Gao J F, Xu L 2007 Acta Phys. Sin. 56 5124 (in Chinese) ［张成芬、高金峰、徐磊 2007 物理学报 56 5124］
[12]	］Zhong Q S, Bao J F, Yu Y B, Liao X F 2009 Chin. Phys. Lett. 25 2812
[13]	］Vapnik V N 2000 The nature of statistical learning theory (2nd ed) (New York: Springer-Vedag) p125
[14]	］Suykens J A K, Vandewalle J 1999 Int. J. Circ. Theor. Appl. 27 605
[15]	］Ye M Y 2005 Acta Phys. Sin. 54 30 (in Chinese) ［叶美盈 2005 物理学报 54 30 ］
[16]	］Liu H, Liu D, Ren H P 2005 Acta Phys. Sin. 54 4019 (in Chinese) ［刘涵、刘丁、任海鹏 2005 物理学报 54 4019］
[17]	］Podlubny I 1999 Fractional differential equations (1st ed) (New York: Academic Press) p41
[18]	］Matignon D 1996 IMACS- SMC Proceedings, Lille, France, July, 1996 p963
[19]	］Ahmed E, El-Sayed A M A, El-Saka H A A 2007 J. Math. Anal. Appl. 325 542

[1]	Liang Ke-Da, Liu Teng-Fei, Chang Zhe, Zhang Meng, Li Zhi-Xin, Huang Song-Song, Wang Jing. Inversion models of internal solitary wave propagation speed in ocean based on least squares method and support vector machine. Acta Physica Sinica, 2023, 72(2): 028301. doi: 10.7498/aps.72.20221633
[2]	Gao Fei, Hu Dao-Nan, Tong Heng-Qing, Wang Chuan-Mei. Chaotic analysis of fractional Willis delayed aneurysm system. Acta Physica Sinica, 2018, 67(15): 150501. doi: 10.7498/aps.67.20180262
[3]	Tang Zhou-Jin, Peng Tao, Wang Wen-Bo. A local least square support vector machine prediction algorithm of small scale network traffic based on correlation analysis. Acta Physica Sinica, 2014, 63(13): 130504. doi: 10.7498/aps.63.130504
[4]	Tang Zhou-Jin, Ren Feng, Peng Tao, Wang Wen-Bo. A least square support vector machine prediction algorithm for chaotic time series based on the iterative error correction. Acta Physica Sinica, 2014, 63(5): 050505. doi: 10.7498/aps.63.050505
[5]	Tian Zhong-Da, Gao Xian-Wen, Shi Tong. Combination kernel function least squares support vector machine for chaotic time series prediction. Acta Physica Sinica, 2014, 63(16): 160508. doi: 10.7498/aps.63.160508
[6]	Zhao Yong-Ping, Zhang Li-Yan, Li De-Cai, Wang Li-Feng, Jiang Hong-Zhang. Chaotic time series prediction using filtering window based least squares support vector regression. Acta Physica Sinica, 2013, 62(12): 120511. doi: 10.7498/aps.62.120511
[7]	Xing HongYan, Qi ZhengDong, Xu Wei. Weak signal estimation in chaotic clutter using selective support vector machine ensemble. Acta Physica Sinica, 2012, 61(24): 240504. doi: 10.7498/aps.61.240504
[8]	Wang Fang-Fang, Zhang Ye-Rong. An electromagnetic inverse scattering approach based on support vector machine. Acta Physica Sinica, 2012, 61(8): 084101. doi: 10.7498/aps.61.084101
[9]	Xing Hong-Yan, Cheng Yan-Yan, Xu Wei. Detection of weak target signal with least-squares support vector machine and generalized embedding windows under chaotic background. Acta Physica Sinica, 2012, 61(10): 100506. doi: 10.7498/aps.61.100506
[10]	Wang Rui, Yang Hong. Fractional order chaotic system control based on feedback and multiple least square support vector machines. Acta Physica Sinica, 2011, 60(7): 070508. doi: 10.7498/aps.60.070508
[11]	Chen Qiang, Ren Xue-Mei. Chaos modeling and real-time online prediction of permanent magnet synchronous motor based on multiple kernel least squares support vector machine. Acta Physica Sinica, 2010, 59(4): 2310-2318. doi: 10.7498/aps.59.2310
[12]	Xing Hong-Yan, Jin Tian-Li. Weak signal estimation in chaotic clutter using wavelet analysis and symmetric LS-SVM regression. Acta Physica Sinica, 2010, 59(1): 140-146. doi: 10.7498/aps.59.140
[13]	Zhang Jun-Feng, Hu Shou-Song. Chaotic time series prediction based on multi-kernel learning support vector regression. Acta Physica Sinica, 2008, 57(5): 2708-2713. doi: 10.7498/aps.57.2708
[14]	. Prediction of chaotic time series based on selective support vector machine ensemble. Acta Physica Sinica, 2007, 56(12): 6820-6827. doi: 10.7498/aps.56.6820
[15]	Zhang Jia-Shu, Dang Jian-Liang, Li Heng-Chao. Local support vector machine prediction of spatiotemporal chaotic time series. Acta Physica Sinica, 2007, 56(1): 67-77. doi: 10.7498/aps.56.67
[16]	Cui Wan-Zhao, Zhu Chang-Chun, Bao Wen-Xing, Liu Jun-Hua. Prediction of the chaotic time series using support vector machines for fuzzy rule-based modeling. Acta Physica Sinica, 2005, 54(7): 3009-3018. doi: 10.7498/aps.54.3009
[17]	Ye Mei-Ying, Wang Xiao-Dong, Zhang Hao-Ran. Chaotic time series forecasting using online least squares support vector machine regression. Acta Physica Sinica, 2005, 54(6): 2568-2573. doi: 10.7498/aps.54.2568
[18]	Ye Mei-Ying. Control of chaotic system based on least squares support vector machine modeling. Acta Physica Sinica, 2005, 54(1): 30-34. doi: 10.7498/aps.54.30
[19]	Liu Han, Liu Ding, Ren Hai-Peng. Chaos control based on least square support vector machines. Acta Physica Sinica, 2005, 54(9): 4019-4025. doi: 10.7498/aps.54.4019
[20]	Cui Wan-Zhao, Zhu Chang-Chun, Bao Wen-Xing, Liu Jun-Hua. Prediction of the chaotic time series using support vector machines. Acta Physica Sinica, 2004, 53(10): 3303-3310. doi: 10.7498/aps.53.3303

Catalog

Vol. 59, Issue 5 - 2010-03-05

Metrics

Abstract views: 8734
PDF Downloads: 938
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板