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As is well known, chaos synchronization has a good performance in secret communication. However, in most existing researches, chaos synchronization is realized between master chaotic system and slave chaotic system with real-time communication. A lot of network bandwidths are wasted in useless communication which may bring great economic costs and increase the likelihood of network congestion. In this paper, the synchronization for the heterogeneous master-slave system is studied. Compared with the homogeneous synchronization, the heterogeneous synchronization has a broad application prospect. Then the sampling controller based on event trigger is designed to achieve the heterogeneous master-slave synchronization which can save network bandwidth, with the control performance maintained. Because transmission time delay is universal in communication system, the delay model of the system is constructed and utilized firstly. Based on the proposed system model, the master-slave heterogeneous synchronization problem is equivalently converted into the asymptotical stability problem of a time-delay system by using the input delayed approach. Then, according to the Lyapunov stability theory and linear matrix inequality, we may rigouously prove that the synchronization of heteogeneous master-slave chaotic system can be achieved. Meanwhile, the heterogeneous master-slave system synchronization conditions and sampling controller can be given based on the constructing Lyapunov-Krasovskii functional with the Wirtinger inequality and free weight matrix method. The sampling controller actually is a stateback controller. But for the purpose of reducing the network usage rate, wheter the state can be transmitted can be determined by the event-triggered rules. The event-triggered rules are designed based on the error state between master chaotic system and slave chaotic system, and the synchronization performance index can be determined by choosing the system parameter. The designed sampling controller updates the control parameters when the event-triggered rules are satisfied. Finally, numerical simulation experiments are employed to verify the correctness and effectiveness of the proposed method. Results indicate that the hetergeneous master-slave chaotic system with transimission time delay can indeed achieve synchronization by event-triggerd sample control. Moreover, the number of communications between master chaotic system and slave chaotic system is less than before and the synchroization performance is also at an idea level.
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Keywords:
- heterogeneous chaotic system /
- master-slave synchronization /
- event-triggered /
- network delay
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[11] Hu C, Yu J 2016 Chaos, Solitons Fractals 91 262
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[15] Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese)[蔡娜, 井元伟, 张嗣瀛2009物理学报58 802]
[16] Huang L L, Qi X 2013 Acta Phys. Sin 62 080507 (in Chinese)[黄丽莲, 齐雪2013物理学报62 080507]
[17] Åström K J, Bernhardsson B 1999 Proceedings of the 14th IFAC World Congress Beijing, China, July 25-27, 1999 p301
[18] Heemels W, Donkers M C F, Teel A R 2013 IEEE Trans. Autom. Control 58 847
[19] Anta A, Tabuada P 2010 IEEE Trans. Autom. Control 55 2030
[20] Mazo M, Anta A, Tabuada P 2010 Automatica 46 1310
[21] Wang X F, Lemmon M D 2009 IEEE Trans. Autom. Control 54 452
[22] Mu N K, Liao X F, Huang T W 2015 IEEE Trans. Circuits Syst. Express Briefs 62 1007
[23] Zhu W, Jiang Z P 2015 IEEE Trans. Autom. Control 60 1362
[24] Wen G H, Chen M Z Q, Yu X H 2016 IEEE Trans. Circuits Syst. Express Briefs 63 304
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[1] Zhang H G, Liu D R, Wang Z L 2009 Controlling Chaos:Suppression, Synchronization and Chaotification (London:Springer) pp1-10
[2] Zhang H G, Xie X P, Wang X Y 2010 Chin. Phys. B 19 060504
[3] Yang J, Qiu Z K, Li X, Zhuang Z W 2011 IET Signal Process. 5 748
[4] Jia H Y, Chen Z Q, Qi G Y 2014 IEEE Trans. Circuits Syst. Regul. Pap. 61 845
[5] Zheng S 2015 ISA Trans. 58 20
[6] He S B, Sun K H, Wang H H 2016 Physica A 461 812
[7] Zhang H G, Xie Y H, Wang Z L, Zheng C D 2007 IEEE Trans. Neural Netw. Learn. Syst. 18 1841
[8] Zhang H G, Ma T D, Huang G B, Wang Z L 2010 IEEE Trans. Syst. Man Cybern. Part B Cybern. 40 831
[9] Ma D Z, Zhan H G, Wang Z S, Feng J 2010 Chin. Phys. B 19 050506
[10] Zhang H G, Huan W, Wang Z L, Chai T Y 2006 Phys. Lett. A 350 363
[11] Hu C, Yu J 2016 Chaos, Solitons Fractals 91 262
[12] Lu J G, Hill D J 2008 IEEE Trans. Circuits Syst. Express Briefs 55 586
[13] Meng J, Wang X Y 2008 Acta Phys. Sin. 57 726 (in Chinese)[孟娟, 王兴元2008物理学报57 726]
[14] Meng J, Wang X Y 2009 Acta Phys. Sin. 58 819 (in Chinese)[孟娟, 王兴元2009物理学报58 819]
[15] Cai N, Jing Y W, Zhang S Y 2009 Acta Phys. Sin. 58 802 (in Chinese)[蔡娜, 井元伟, 张嗣瀛2009物理学报58 802]
[16] Huang L L, Qi X 2013 Acta Phys. Sin 62 080507 (in Chinese)[黄丽莲, 齐雪2013物理学报62 080507]
[17] Åström K J, Bernhardsson B 1999 Proceedings of the 14th IFAC World Congress Beijing, China, July 25-27, 1999 p301
[18] Heemels W, Donkers M C F, Teel A R 2013 IEEE Trans. Autom. Control 58 847
[19] Anta A, Tabuada P 2010 IEEE Trans. Autom. Control 55 2030
[20] Mazo M, Anta A, Tabuada P 2010 Automatica 46 1310
[21] Wang X F, Lemmon M D 2009 IEEE Trans. Autom. Control 54 452
[22] Mu N K, Liao X F, Huang T W 2015 IEEE Trans. Circuits Syst. Express Briefs 62 1007
[23] Zhu W, Jiang Z P 2015 IEEE Trans. Autom. Control 60 1362
[24] Wen G H, Chen M Z Q, Yu X H 2016 IEEE Trans. Circuits Syst. Express Briefs 63 304
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