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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.
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Keywords:
- multi-scroll chaotic system /
- adaptive fuzzy control /
- modified function projective lag synchronization
[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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[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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