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According to the stability of fractional order linear systems theory, the system is decomposed into stable linear parts and the corresponding nonlinear parts. The active controller is designed to compensate the nonlinear parts, and the fractional order chaotic system is suppressed to an equilibrium point. In order to improve the compensation ability of active controller, a multiple least square support vector machine (M-LS-SVM) regression model is presented based on feedback. The subtractive clustering is adopted to divide the input space into several sub-spaces, and sub-models are built by a LS-SVM in each sub-space. In order to minimize the severe correlation among sub-models and to improve the accuracy and the robustness of the model, the sub-models are combined by principal component regression (PCR).The experiment result shows that by using the method the compensation accuracy and the system response indices can be improved.
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Keywords:
- fractional order /
- chaotic system /
- multiple least square support vector machines /
- feedback
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[2] Gao X, Yu J B 2005 Chaos, Solitons Fract. 24 1097
[3] Li C G, Peng J 2004 Chaos, Solitons Fract. 22 443
[4] Gao X, Yu J B 2005 Chin. Phys. 14 908
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[6] Lai X Q, Li Z H, Yuan B, Wang H, Ye Q, Zhao Y R 2010 Acta Phys. Sin. 59 2256 (in Chinese) [来新泉、李祖贺、袁 冰、王 慧、叶 强、赵永瑞 2010 物理学报 59 2256]
[7] Ma T D, Zhang H G, J Fu 2009 Dynamics of Continuous, Discrete and impulsive Systems Series B: Applications & Algorithms. 16 215
[8] Li C P, Deng W H 2006 Int J Modern Phys. B 20 791
[9] Mohammad Saleh Tavazoei, Mohammad Haeri 2008 Physica A 387 57
[10] Qi D L, Yang J, Zhang J L 2010 Chin. Phys. B 19 100506
[11] Hu J B, H Y, Zhao L D 2008 Acta Phys.Sin. 57 7522 (in Chinese) [胡建兵、韩 炎、赵灵冬 2008 物理学报 57 7522]
[12] Zhang R X, Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6039 (in Chinese) [张若洵、杨 洋、杨世平 2009 物理学报 58 6039] 〖13] 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]
[13] Gao X, Yu J B 2005 Chin. Phys. 14 908
[14] Zhong Q S, Bao J F, Yu Y B, Liao X F 2009 Chin. Phys. Lett. 25 2812
[15] Serdar E H 2007 IEEE Trans on Automatic Control. 52 1964
[16] Wen X J, Wu Z M, Lu J G 2008 IEEE Trans on Circuits and Systems II 55 1178
[17] Ma T D, Zhang H G, J Fu 2008 Chin. Phys. B 17 4407
[18] Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456 (in Chinese) [闵富红、余 杨、葛曹君 2009 物理学报 58 1456]
[19] Suykens J A K, Vandewalle J 1999 Int. J. Circ. Theor. Appl. 27 605
[20] Yan X M, Liu D 2010 Acta Phys. Sin. 59 3043 (in Chinese)[阎晓妹、刘 丁 2010 物理学报 59 3043]
[21] Yuan P, Mao Z Z, Wang F L 2006 Journal of System Simulation 18 1458 (in Chinese)[袁 平、毛志忠、王福利 2006 系统仿真学报 18 1458]
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[1] Ge Z M, Ou C Y 2007 Chaos Soliton.Fract. 34 262
[2] Gao X, Yu J B 2005 Chaos, Solitons Fract. 24 1097
[3] Li C G, Peng J 2004 Chaos, Solitons Fract. 22 443
[4] Gao X, Yu J B 2005 Chin. Phys. 14 908
[5] Zhu S P, Qian F C, Liu D 2010 Acta Phys. Sin. 59 2250(in Chinese)[朱少平、钱富才、刘 丁 2010 物理学报 59 2250]
[6] Lai X Q, Li Z H, Yuan B, Wang H, Ye Q, Zhao Y R 2010 Acta Phys. Sin. 59 2256 (in Chinese) [来新泉、李祖贺、袁 冰、王 慧、叶 强、赵永瑞 2010 物理学报 59 2256]
[7] Ma T D, Zhang H G, J Fu 2009 Dynamics of Continuous, Discrete and impulsive Systems Series B: Applications & Algorithms. 16 215
[8] Li C P, Deng W H 2006 Int J Modern Phys. B 20 791
[9] Mohammad Saleh Tavazoei, Mohammad Haeri 2008 Physica A 387 57
[10] Qi D L, Yang J, Zhang J L 2010 Chin. Phys. B 19 100506
[11] Hu J B, H Y, Zhao L D 2008 Acta Phys.Sin. 57 7522 (in Chinese) [胡建兵、韩 炎、赵灵冬 2008 物理学报 57 7522]
[12] Zhang R X, Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6039 (in Chinese) [张若洵、杨 洋、杨世平 2009 物理学报 58 6039] 〖13] 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]
[13] Gao X, Yu J B 2005 Chin. Phys. 14 908
[14] Zhong Q S, Bao J F, Yu Y B, Liao X F 2009 Chin. Phys. Lett. 25 2812
[15] Serdar E H 2007 IEEE Trans on Automatic Control. 52 1964
[16] Wen X J, Wu Z M, Lu J G 2008 IEEE Trans on Circuits and Systems II 55 1178
[17] Ma T D, Zhang H G, J Fu 2008 Chin. Phys. B 17 4407
[18] Min F H, Yu Y, Ge C J 2009 Acta Phys. Sin. 58 1456 (in Chinese) [闵富红、余 杨、葛曹君 2009 物理学报 58 1456]
[19] Suykens J A K, Vandewalle J 1999 Int. J. Circ. Theor. Appl. 27 605
[20] Yan X M, Liu D 2010 Acta Phys. Sin. 59 3043 (in Chinese)[阎晓妹、刘 丁 2010 物理学报 59 3043]
[21] Yuan P, Mao Z Z, Wang F L 2006 Journal of System Simulation 18 1458 (in Chinese)[袁 平、毛志忠、王福利 2006 系统仿真学报 18 1458]
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