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针对一类含有不确定参数的时变时滞系统的同步控制问题，提出了一种滑模自适应鲁棒控制方法. 基于Lyapunov稳定性理论和滑模自适应控制方法，设计出滑模自适应鲁棒控制器和参数自适应率. 所设计的单一控制器适用于一类分数阶超混沌系统的同步性控制问题，它不仅具有较强的抗噪声能力而且对于时变时滞系统也具有良好的控制能力，因此该控制器具有较好的实用价值. 此外，通过在系统的输入量中引入一个补偿量，用以消除系统中所存在的不确定性和外界扰动的影响，从而实现不确定性分数阶超混沌系统的同步，并且将系统的同步误差控制在任意小范围内. 最后，对带有外界噪声扰动、系统参数不确定的时变时滞Chen分数阶超混沌系统进行了数值仿真，经过短暂的时间，响应系统与驱动系统同步，进而验证了所提出的控制方法的有效性.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.
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Keywords:
- fractional-order hyper-chaotic systems /
- adaptive sliding robust mode controls /
- uncertain time-varying-delay systems
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[8] Zhang R X, Yang S P 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵, 杨世平 2010 59 1549]
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[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
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[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)]
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[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)]
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