-
In view of a class of synchronization problems about uncertain and variable time-delay systems, this paper puts forward a method of adaptive sliding robust control. Based on the Lyapunov stability theory and adaptive sliding mode control methods, the adaptive sliding robust controllers and the parameter adaptive rate are designed. A single controller designed by the synchronous control method is applicable to the synchronizing of a class of fractional-order hyper-chaotic systems, and it has a great ability to resist noise-perturbed. What is more, it can also well control the time-varying time-delay systems. So the controller is of highly practical value. Furthermore, by introducing a certain amount of compensation into the system, the influences of the uncertainty and the noise-disturbance can be eliminated, thus the synchronization of the uncertainty fractional-order hyper-chaotic system is realized. In addition, the control of the synchronous errors of the systems can be stable in arbitrarily small domain. Finally, time-varying and time-delay fractional-order Chen's hyper-chaotic systems with the external noisy disturbances and uncertain parameters are numerically simulated, and the effectiveness of the proposed control method is verified.
-
Keywords:
- fractional-order hyper-chaotic systems /
- adaptive sliding robust mode controls /
- uncertain time-varying-delay systems
[1] Pecora L M, Carroll T L 1991 IEEE Trans. Circ. Syst. 38 453
[2] Tour J M, Tao H 2008 Nature 453 42
[3] Balasubramaniam P, Lakshmanan S 2009 Nonlinear Anal. Hybrid Syst. 3 749
[4] Itoh M, Chua L O 2008 Int. J. Bifur. Chaos 18 3183
[5] Wang D F, Zhang J Y, Wang X Y 2013 Chin. Phys. B 22 100504
[6] Yuan L G, Yang Q G 2012 Commun. Nonlinear Sci. Numer. Simul. 17 305
[7] Li C L, Luo X S 2009 Acta Phys. Sin. 58 3759 (in Chinese) [李春来, 罗晓曙 2009 58 3759]
[8] Zhang R X, Yang S P 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵, 杨世平 2010 59 1549]
[9] Aghababa M P 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2670
[10] Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若洵 2011 60 050510]
[11] Zhen R, Liu J, Wu X L, Wu X J, Zhu Q M, Wang Y, Nouri H 2013 Int. J. Model. Ident. Control 20 164
[12] 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 59 2250]
[13] Li R H, Chen W S 2013 Chin. Phys. B 22 040503
[14] Cui Z H, Cai X J, Zeng J C 2012 Int. J. Comput. Appl. Technol. 43 366
[15] Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 59 2305]
[16] Xu B R 2013 Acta Phys. Sin. 62 190506 (in Chinese) [许碧荣 2013 62 190506]
[17] Mahmoud G M, Mahmoud E E 2012 Nonlinear Dyn. 67 1613
[18] Kim S H, Park P, Jeong C 2010 IET Control Theory Appl. 4 1828
[19] Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502
[20] Kiani B A, Fallahi K, Pariz N, Leung H 2009 Commun. Nonlinear Sci. Numer. Simul. 14 863
[21] Zhou P, Zhu W 2011 Nonlinear Anal. RWA 12 811
[22] Ma S Q, Lu Q S, Feng Z S 2010 Int. J. Nonlinear Mech. 45 659
[23] Qiao Z M 2007 Ph. D. Dissertation (Hefei: Anhui University) (in Chinese) [乔宗敏 2007 博士学位论文 (合肥: 安徽大学)]
[24] Hu J B 2008 Ph. D. Dissertation (Taiyuan: North University of China) (in Chinese) [胡建兵 2008 博士学位论文 (太原: 中北大学)]
-
[1] Pecora L M, Carroll T L 1991 IEEE Trans. Circ. Syst. 38 453
[2] Tour J M, Tao H 2008 Nature 453 42
[3] Balasubramaniam P, Lakshmanan S 2009 Nonlinear Anal. Hybrid Syst. 3 749
[4] Itoh M, Chua L O 2008 Int. J. Bifur. Chaos 18 3183
[5] Wang D F, Zhang J Y, Wang X Y 2013 Chin. Phys. B 22 100504
[6] Yuan L G, Yang Q G 2012 Commun. Nonlinear Sci. Numer. Simul. 17 305
[7] Li C L, Luo X S 2009 Acta Phys. Sin. 58 3759 (in Chinese) [李春来, 罗晓曙 2009 58 3759]
[8] Zhang R X, Yang S P 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵, 杨世平 2010 59 1549]
[9] Aghababa M P 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2670
[10] Cao H F, Zhang R X 2011 Acta Phys. Sin. 60 050510 (in Chinese) [曹鹤飞, 张若洵 2011 60 050510]
[11] Zhen R, Liu J, Wu X L, Wu X J, Zhu Q M, Wang Y, Nouri H 2013 Int. J. Model. Ident. Control 20 164
[12] 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 59 2250]
[13] Li R H, Chen W S 2013 Chin. Phys. B 22 040503
[14] Cui Z H, Cai X J, Zeng J C 2012 Int. J. Comput. Appl. Technol. 43 366
[15] Zhao L D, Hu J B, Liu X H 2010 Acta Phys. Sin. 59 2305 (in Chinese) [赵灵冬, 胡建兵, 刘旭辉 2010 59 2305]
[16] Xu B R 2013 Acta Phys. Sin. 62 190506 (in Chinese) [许碧荣 2013 62 190506]
[17] Mahmoud G M, Mahmoud E E 2012 Nonlinear Dyn. 67 1613
[18] Kim S H, Park P, Jeong C 2010 IET Control Theory Appl. 4 1828
[19] Li Z J, Zeng Y C 2013 Chin. Phys. B 22 040502
[20] Kiani B A, Fallahi K, Pariz N, Leung H 2009 Commun. Nonlinear Sci. Numer. Simul. 14 863
[21] Zhou P, Zhu W 2011 Nonlinear Anal. RWA 12 811
[22] Ma S Q, Lu Q S, Feng Z S 2010 Int. J. Nonlinear Mech. 45 659
[23] Qiao Z M 2007 Ph. D. Dissertation (Hefei: Anhui University) (in Chinese) [乔宗敏 2007 博士学位论文 (合肥: 安徽大学)]
[24] Hu J B 2008 Ph. D. Dissertation (Taiyuan: North University of China) (in Chinese) [胡建兵 2008 博士学位论文 (太原: 中北大学)]
Catalog
Metrics
- Abstract views: 6761
- PDF Downloads: 720
- Cited By: 0
下载:
