带未知扰动的多涡卷混沌系统修正函数时滞投影同步

刘恒; 余海军; 向伟

doi:10.7498/aps.61.180503

摘要

研究了带有未知外部扰动的不同多涡卷混沌系统修正函数时滞投影同步问题. 基于Lyapunov稳定性理论, 采用模糊自适应控制的方法设计自适应同步控制器及参数的更新规则. 该控制器在实现混沌系统修正函数时滞投影同步的同时对外界扰动的变化能保持较好的稳定性. 数值仿真的结果进一步验证了该方法的有效性.

关键词:

In this paper, we treat the modified function projective lag synchronization between two non-identical multi-scroll chaotic systems with unknown disturbances. By utilizing the lyapunov stability theory, the fuzzy adaptive controller and parameter update law are derived to make the state of chaotic system achieve modified function projective lag synchronization. The controller can keep the systems stable even when the disturbance changes. Finally numerical simulations are performed to show the effectiveness of the proposed method.

Keywords:

multi-scroll chaotic system /
adaptive fuzzy control /
modified function projective lag synchronization

作者及机构信息

1.
淮南师范学院数学与计算科学系, 淮南 232038;

2.
淮南师范学院物理与电子信息系, 淮南 232038

基金项目: 安徽高校省级自然科学研究项目(批准号: KJ2011Z359)和安徽省高校省级优秀青年人才基金项目(批准号: 2012SQRL179)资助的课题.

Authors and contacts

1.
Department of Mathematics and Computer Science, Huainan Normal University, Huainan 232038, China;

2.
Departement of Physics and Electronic Information, Huainan Normal University, Huainan 232038, China

Funds: Project supported by the Natural Science Foundation of the Anhui Higher Education Institutions of China (Grant No. KJ2011Z359) and the Natural Science Foundation of the Anhui Higher Education Excellent Young Talents of China (Grant No. 2012SQRL179).

参考文献

[1]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Rulkov N F, Sushchik M M, Tsimring L S 1995 Phys. Rev. E 51 980
[3]	Rosenblum M G, Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 4193
[4]	Hramov A E, Koronovskii A A 2004 Chaos 14 603
[5]	Mainieri R, Rehacek J 1999 Phys. Rev. Lett. 82 3042
[6]	Xiang W, Chen F Q 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 2970
[7]	Li J F, Li N 2011 Acta Phys. Sin. 60 080507 (in Chinese) [李建芬, 李农 2011 物理学报 60 080507]
[8]	Chen Y, An H L, Li Z B 2008 Appl. Math. Comput. 197 96
[9]	Du H Y, Zeng Q H, Wang C 2009 Chaos, Solitons and Fractals 42 2399
[10]	Du H Y, Zeng Q H, Lü N 2010 Phys. Lett. A 374 1493
[11]	Wu X J, Lu H T 2011 Chaos, Solitons and Fractals. 44 802
[12]	Lü J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[13]	Chen G R, Lü J H 2003 Dynamics of the Lorenz Systems Family: Analysis, Control and Synchronization (Beijing: Science Press) chapt. 8 (in Chinese) [陈关荣, 吕金虎 2003 Lorenz 系统族的动力学分析、控制与同步(北京: 科学出版社) 第八章]
[14]	Lü J H, Chen G R, Cheng D Z 2002 Int. J. Bifure. Chaos 12 2917
[15]	Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits Syst. I 40 861
[16]	Lü J H, Yu X H, Chen G R 2003 IEEE Trans. Circuits Syst. I 50 198
[17]	Lü J H, Chen G R, Yu X H, Leung H 2004 IEEE Trans. Circuits Syst. I 51 2476
[18]	Lü J H, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[19]	Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui M A 2008 Phys. Lett. A 372 3234
[20]	Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I 53 149
[21]	Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 12 775
[22]	Essounbouli N, Hamzaoui A, Zaytoon J 2006 Control Intell. Systems 34 12
[23]	Tong S C, Tang J, Wang T 2000 Fuzzy Sets and Systems 111 153
[24]	Boulkroune A, Tadjine M, M'Saad M, Farza M 2010 Fuzzy Sets and Systems 161 797
[25]	Meng J, Wang X Y 2009 Acta Phys. Sin. 58 819 (in Chinese) [孟元, 王兴元 2009 物理学报 58 819]
[26]	Wang L X 1994 Adaptive Fuzzy Systems and Control: Design and Stability Analysis (NJ: Hall, Englewood Cliffs) pp30-40

施引文献

[1]	Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[2]	Rulkov N F, Sushchik M M, Tsimring L S 1995 Phys. Rev. E 51 980
[3]	Rosenblum M G, Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 4193
[4]	Hramov A E, Koronovskii A A 2004 Chaos 14 603
[5]	Mainieri R, Rehacek J 1999 Phys. Rev. Lett. 82 3042
[6]	Xiang W, Chen F Q 2011 Commun. Nonlinear Sci. Numer. Simulat. 16 2970
[7]	Li J F, Li N 2011 Acta Phys. Sin. 60 080507 (in Chinese) [李建芬, 李农 2011 物理学报 60 080507]
[8]	Chen Y, An H L, Li Z B 2008 Appl. Math. Comput. 197 96
[9]	Du H Y, Zeng Q H, Wang C 2009 Chaos, Solitons and Fractals 42 2399
[10]	Du H Y, Zeng Q H, Lü N 2010 Phys. Lett. A 374 1493
[11]	Wu X J, Lu H T 2011 Chaos, Solitons and Fractals. 44 802
[12]	Lü J H, Chen G R 2002 Int. J. Bifur. Chaos 12 659
[13]	Chen G R, Lü J H 2003 Dynamics of the Lorenz Systems Family: Analysis, Control and Synchronization (Beijing: Science Press) chapt. 8 (in Chinese) [陈关荣, 吕金虎 2003 Lorenz 系统族的动力学分析、控制与同步(北京: 科学出版社) 第八章]
[14]	Lü J H, Chen G R, Cheng D Z 2002 Int. J. Bifure. Chaos 12 2917
[15]	Suykens J A K, Vandewalle J 1993 IEEE Trans. Circuits Syst. I 40 861
[16]	Lü J H, Yu X H, Chen G R 2003 IEEE Trans. Circuits Syst. I 50 198
[17]	Lü J H, Chen G R, Yu X H, Leung H 2004 IEEE Trans. Circuits Syst. I 51 2476
[18]	Lü J H, Han F L, Yu X H, Chen G R 2004 Automatica 40 1677
[19]	Lü J H, Murali K, Sinha S, Leung H, Aziz-Alaoui M A 2008 Phys. Lett. A 372 3234
[20]	Lü J H, Yu S M, Leung H, Chen G R 2006 IEEE Trans. Circuits Syst. I 53 149
[21]	Lü J H, Chen G R 2006 Int. J. Bifur. Chaos 12 775
[22]	Essounbouli N, Hamzaoui A, Zaytoon J 2006 Control Intell. Systems 34 12
[23]	Tong S C, Tang J, Wang T 2000 Fuzzy Sets and Systems 111 153
[24]	Boulkroune A, Tadjine M, M'Saad M, Farza M 2010 Fuzzy Sets and Systems 161 797
[25]	Meng J, Wang X Y 2009 Acta Phys. Sin. 58 819 (in Chinese) [孟元, 王兴元 2009 物理学报 58 819]
[26]	Wang L X 1994 Adaptive Fuzzy Systems and Control: Design and Stability Analysis (NJ: Hall, Englewood Cliffs) pp30-40

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