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通过设计一个非线性反馈控制器,实现了分数阶混沌系统的同步.与其他的分数阶混沌系统同步方法相比,提出的控制器设计方法保留了部分误差系统中的非线性项,而没有完全抵消同步误差系统的非线性项,有效改善了误差系统的控制性能.同时,应用区间分数阶线性时不变系统稳定性原理和线性矩阵不等式技术,得到了一个新的分数阶混沌系统同步的充分条件,进而获得的控制器保证了混沌系统同步.仿真结果验证了提出方法的有效性.
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关键词:
- 区间分数阶时不变系统 /
- 分数阶混沌系统 /
- 混沌同步
Synchronization of fractional-order chaotic systems is investigated by designing a novel nonlinear feedback controller. Compared with the previous reports, the controlled synchronization error system does not need to turn into a linear system and the performance is improved effectively. Furthermore, a novel sufficient stabilization criterion for fractional-order chaotic systems is proposed by introducing a stabilization criterion of an interval fractional-order linear time-invariant system and using the linear matrix inequality technique. Consequently, the chaotic synchronization is ensured. The simulation result verifies the effectiveness of the proposed method.-
Keywords:
- interval fractional-order time-invariant system /
- fractional-order chaotic system /
- chaotic synchronization
[1] Zhu H, Zhou S, Zhang J 2009 Chaos Soliton Fract. 39 1595
[2] Li C, Peng G 2004 Chaos Soliton Fract. 22 443
[3] Lu J G 2006 Phys. Lett. A 354 305
[4] Xu C, Feng J W, Austin F, Zhang W Q 2009 Int. J. Nonlin. Sci. Numer. Simul. 10 1517
[5] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[6] Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3742
[7] Zhang H G, Liu D R, Wang Z L 2009 Controlling Chaos: Suppression, Synchronization and Chaotification (New York:Springer Verlag) p38
[8] Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlin. Sci. Numer. Simul. 15 3536
[9] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵、杨世平、刘永利 2010 59 1549]
[10] Zhou P, Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese) [周 平、邝 菲 2010 59 6851]
[11] Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 110509
[12] Zhang R X, Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6039 (in Chinese) [张若洵、杨 洋、杨世平 2009 58 6039]
[13] Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙 宁、张化光、王智良 2011 60 050511]
[14] Lu J G, Chen G R 2009 IEEE Trans. Aut. Contr. 54 1294
[15] Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) p18
[16] Matignon D 1996 Computational Engineering in System Application (Lille: IEEE) p963
[17] Moze M, Sabatier J, Oustaloup A 2005 Proceedings of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Long Beach: ASME) p1611
[18] Khargonekar P P, Petersen I R, Zhou K 1990 IEEE Trans. Autom. Control 35 356
[19] Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM) p7
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[1] Zhu H, Zhou S, Zhang J 2009 Chaos Soliton Fract. 39 1595
[2] Li C, Peng G 2004 Chaos Soliton Fract. 22 443
[3] Lu J G 2006 Phys. Lett. A 354 305
[4] Xu C, Feng J W, Austin F, Zhang W Q 2009 Int. J. Nonlin. Sci. Numer. Simul. 10 1517
[5] Pecora L M, Carroll T L 1990 Phys. Rev. Lett. 64 821
[6] Zhang H G, Ma T D, Fu J, Tong S C 2009 Chin. Phys. B 18 3742
[7] Zhang H G, Liu D R, Wang Z L 2009 Controlling Chaos: Suppression, Synchronization and Chaotification (New York:Springer Verlag) p38
[8] Bhalekar S, Daftardar-Gejji V 2010 Commun. Nonlin. Sci. Numer. Simul. 15 3536
[9] Zhang R X, Yang S P, Liu Y L 2010 Acta Phys. Sin. 59 1549 (in Chinese) [张若洵、杨世平、刘永利 2010 59 1549]
[10] Zhou P, Kuang F 2010 Acta Phys. Sin. 59 6851 (in Chinese) [周 平、邝 菲 2010 59 6851]
[11] Jia L X, Dai H, Hui M 2010 Chin. Phys. B 19 110509
[12] Zhang R X, Yang Y, Yang S P 2009 Acta Phys. Sin. 58 6039 (in Chinese) [张若洵、杨 洋、杨世平 2009 58 6039]
[13] Sun N, Zhang H G, Wang Z L 2011 Acta Phys. Sin. 60 050511 (in Chinese) [孙 宁、张化光、王智良 2011 60 050511]
[14] Lu J G, Chen G R 2009 IEEE Trans. Aut. Contr. 54 1294
[15] Podlubny I 1999 Fractional Differential Equations (San Diego: Academic Press) p18
[16] Matignon D 1996 Computational Engineering in System Application (Lille: IEEE) p963
[17] Moze M, Sabatier J, Oustaloup A 2005 Proceedings of International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (Long Beach: ASME) p1611
[18] Khargonekar P P, Petersen I R, Zhou K 1990 IEEE Trans. Autom. Control 35 356
[19] Boyd S, Ghaoui L E, Feron E, Balakrishnan V 1994 Linear Matrix Inequalities in System and Control Theory (Philadelphia: SIAM) p7
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