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In this paper, a sliding mode control based on an online error correction adaptive SVR is put forward for a class of fractional order chaotic system with nonlinear uncertainty. In order to solve the problem that the uncertainty of the fractional order chaotic system model is difficult to predict, so the nonlinear function of the system is estimated by the offline SVR and the state trace error is forecasted by using incremental learning adaptive online SVR. In addition, the adaptive parameter adjustment law is selected by using the Lyapunov stability theory. Result of simulation of the fractional order Arneodo system shows that the sliding mode control based on the online error correction adaptive SVR can stabilize the nonlinear uncertain fractional order chaotic system with external noise disturbance to an expected state within a limited time. At the same time, both the control performance and the prediction precision of the system's nonlinear function can be improved.
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Keywords:
- fractional order system /
- chaotic system /
- sliding mode control /
- adaptive SVR
[1] Yan X M, Lin D 2010 Acta Phys. Sin. 59 3043 (in Chinese) [阎晓妹, 刘丁 2010 物理学报 59 3043]
[2] Li T Z, Wang Y, Luo M K 2014 Chin. Phys. B 23 080501
[3] Chen D Y, Liu Y X, Ma X Y, Zhang R F 2011 Chin. Phys. B 20 120506
[4] Zhou P, Cheng Y M, Kuang F 2010 Chin. Phys. B 19 090503
[5] Lin T C, Kuo C H, Balas V E. 2011 International Journal of Computers Communications & Control, September 3, 418-427
[6] Zhao J, Chen J J 2009 Control and Decision 24 1559 (in Chinese) [赵俊, 陈建军 2009 控制与决策 24 1559]
[7] Zhang R X, Yang S P 2011 Chin. Phys. B 20 110506
[8] Huang L L, Xin F, Wang L Y 2011 Acta Phys. Sin. 60 010505 (in Chinese) [黄丽莲, 辛方, 王霖郁 2011 物理学报 60 010505]
[9] Chen X R, Liu C X, Wang F Q 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣, 刘崇新, 王发强 2008 物理学报 57 1416]
[10] Zhang B T, Pi Y G 2012 Control and Decision 27 1776 (in Chinese) [张碧陶, 皮佑国 2012 控制与决策 27 1776]
[11] Chen D Y, Zhang R F, Sprott J C, Ma X Y 2012 Nonlinear Dynamics 70 1549
[12] Wang B Q, Lin X L 2009 Computer Engineering and Design 13 3219 (in Chinese) [王勃群, 蔺小林 2009 计算机工程与设计 13 3219]
[13] Xiao H M, Zhao L, Wang C H 2012 Control Theory and Application 28 1621 (in Chinese) [肖会敏, 赵林, 王春花 2012 控制理论与应用 28 1621]
[14] Tang G Y, Pang H P, Sun H Y 2009 Control Theory and Application 8 850 (in Chinese) [唐功友, 逄海萍, 孙慧影 2009 控制理论与应用 8 850]
[15] Xiao H R, Li Y B, Zhou F Y, Han Y Z 2011 Electrical Power System and Computers 99 503
[16] Wang H, Pi D Y, Sun Y X 2007 Neurocomputing 70 952
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[1] Yan X M, Lin D 2010 Acta Phys. Sin. 59 3043 (in Chinese) [阎晓妹, 刘丁 2010 物理学报 59 3043]
[2] Li T Z, Wang Y, Luo M K 2014 Chin. Phys. B 23 080501
[3] Chen D Y, Liu Y X, Ma X Y, Zhang R F 2011 Chin. Phys. B 20 120506
[4] Zhou P, Cheng Y M, Kuang F 2010 Chin. Phys. B 19 090503
[5] Lin T C, Kuo C H, Balas V E. 2011 International Journal of Computers Communications & Control, September 3, 418-427
[6] Zhao J, Chen J J 2009 Control and Decision 24 1559 (in Chinese) [赵俊, 陈建军 2009 控制与决策 24 1559]
[7] Zhang R X, Yang S P 2011 Chin. Phys. B 20 110506
[8] Huang L L, Xin F, Wang L Y 2011 Acta Phys. Sin. 60 010505 (in Chinese) [黄丽莲, 辛方, 王霖郁 2011 物理学报 60 010505]
[9] Chen X R, Liu C X, Wang F Q 2008 Acta Phys. Sin. 57 1416 (in Chinese) [陈向荣, 刘崇新, 王发强 2008 物理学报 57 1416]
[10] Zhang B T, Pi Y G 2012 Control and Decision 27 1776 (in Chinese) [张碧陶, 皮佑国 2012 控制与决策 27 1776]
[11] Chen D Y, Zhang R F, Sprott J C, Ma X Y 2012 Nonlinear Dynamics 70 1549
[12] Wang B Q, Lin X L 2009 Computer Engineering and Design 13 3219 (in Chinese) [王勃群, 蔺小林 2009 计算机工程与设计 13 3219]
[13] Xiao H M, Zhao L, Wang C H 2012 Control Theory and Application 28 1621 (in Chinese) [肖会敏, 赵林, 王春花 2012 控制理论与应用 28 1621]
[14] Tang G Y, Pang H P, Sun H Y 2009 Control Theory and Application 8 850 (in Chinese) [唐功友, 逄海萍, 孙慧影 2009 控制理论与应用 8 850]
[15] Xiao H R, Li Y B, Zhou F Y, Han Y Z 2011 Electrical Power System and Computers 99 503
[16] Wang H, Pi D Y, Sun Y X 2007 Neurocomputing 70 952
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