Adaptive synchronization of uncertain chaotic systems via switching mechanism

doi:10.1088/1674-1056/19/12/120504

中国物理B ›› 2010, Vol. 19 ›› Issue (12): 120504-120504.doi: 10.1088/1674-1056/19/12/120504

Adaptive synchronization of uncertain chaotic systems via switching mechanism

张庆灵¹, 冯毅夫²

(1)Institute of Systems Science, Northeastern University, Shenyang 110819, China; (2)School of Mathematics, Jilin Normal University, Siping 136000, China

收稿日期:2010-02-28 修回日期:2010-05-14 出版日期:2010-12-15 发布日期:2010-12-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60974004).

Adaptive synchronization of uncertain chaotic systems via switching mechanism

Feng Yi-Fu(冯毅夫)^a)†ger and Zhang Qing-Ling(张庆灵)^b)

^a School of Mathematics, Jilin Normal University, Siping 136000, China; ^b Institute of Systems Science, Northeastern University, Shenyang 110819, China

Received:2010-02-28 Revised:2010-05-14 Online:2010-12-15 Published:2010-12-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60974004).

摘要/Abstract

摘要： This paper deals with the problem of synchronization for a class of uncertain chaotic systems. The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error, with unknown growth rate. A logic-based switching mechanism is presented for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on the Lyapunov approach, the adaptation law is determined to tune the controller gain vector online according to the possible nonlinearities. To demonstrate the efficiency of the proposed scheme, the well-known chaotic system namely Chua's circuit is considered as an illustrative example.

Abstract: This paper deals with the problem of synchronization for a class of uncertain chaotic systems. The uncertainties under consideration are assumed to be Lipschitz-like nonlinearity in tracking error, with unknown growth rate. A logic-based switching mechanism is presented for tracking a smooth orbit that can be a limit cycle or a chaotic orbit of another system. Based on the Lyapunov approach, the adaptation law is determined to tune the controller gain vector online according to the possible nonlinearities. To demonstrate the efficiency of the proposed scheme, the well-known chaotic system namely Chua's circuit is considered as an illustrative example.

Key words: chaos synchronization, adaptive synchronization, switching mechanism

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

冯毅夫, 张庆灵. Adaptive synchronization of uncertain chaotic systems via switching mechanism[J]. 中国物理B, 2010, 19(12): 120504-120504.

Feng Yi-Fu(冯毅夫) and Zhang Qing-Ling(张庆灵). Adaptive synchronization of uncertain chaotic systems via switching mechanism[J]. Chin. Phys. B, 2010, 19(12): 120504-120504.

参考文献 31

[1]	Pecora L and Carroll T 1990 Phys. Rev. Lett. 64 821
[2]	Chen G and Dong X 1998 From Chaos to Order (Singapore: World Scientific)
[3]	Fradkov A L and Pogromsky A Yu 1998 Introduction to Control of Oscillations and Chaos (Singapore: World Scientific)
[4]	Cuomo K M, Oppenheim A V and Strogatz S H 1993 IEEE Trans. Circuits Syst 40 626
[5]	Dedieu H, Kennedy M P and Hasler M 1993 IEEE Trans. Circuits Syst. II 40 634
[6]	Chua L O, Yang T, Zhong G Q and Wu C W 1996 IEEE Trans. Circuits Syst. I Fundamental Theor. Appl. 43 862
[7]	Dedieu H and Ogorzalek M J 1997 IEEE Trans. Circuits Syst. I 44 948
[8]	Kolumban G, Kennedy M P and Chua L O 1997 IEEE Trans. Circuits Syst. I 44 927
[9]	Kolumban G, Kennedy M P and Chua L O 1998 IEEE Trans. Circuits Syst. I 45 1129
[10]	Ott E, Grebogi C and Yorke J A 1993 Phys. Rev. Lett. 70 3872
[11]	Boccaletti S, Grobogi C, Lai Y C, Maricini H and Maza D 2000 Phys. Rep. 329 103
[12]	Yang S K, Chen C L and Yau H T 2002 Chaos, Solitons and Fractals 13 767
[13]	Hwang C C, Hsieh J Y and Lin R S 1997 Chaos, Solitons and Fractals 8 1507
[14]	Bernardo M D 1996 Int. J. Bifur. Chaos 6 557
[15]	Tain Y C and Tade M O and Levy D 2002 Phys. Lett. A 296 87
[16]	Hwang C C, Fung R F, Hsieh J Y and Li W J 1999 Int. J. Eng. Sci. 37 1893
[17]	Solak E, Morgül Ö and Ersoy U 2001 Phys. Lett. A 279 47
[18]	John J K and Amritkar A E 1994 Int. J. Bifur. Chaos 4 1687
[19]	Chen S and Lü J 2002 Chaos, Solitons and Fractals 14 643
[20]	Wang C and Ge S 2001 Chaos, Solitons and Fractals 12 1199
[21]	Lei H and Lin W 2007 Syst. Control Lett. 56 529
[22]	Isidori A 1995 Nonlinear Control Systems (United Kingdom: Springer-Verlag)
[23]	Tan W and Wang Y N 2005 Chin. Phys. 14 72
[24]	Hua C C and Guan X P 2004 Chin. Phys. 13 1391
[25]	Li Z and Shi S J 2004 Chin. Phys. 13 1221
[26]	Li G H, Zhou S P and Xu D M 2004 Chin. Phys. 13 168
[27]	Li R, Duan Z S and Chen G R 2009 Chin. Phys. 18 106
[28]	Zhou P, Wei L J and Cheng X F 2009 Chin. Phys. 18 2674
[29]	Wang J W, Chen A M, Zhang J J, Yuan Z J and Zhou T S 2009 Chin. Phys. B 18 1294
[30]	Tang Y, Zhong H H and Fang J A 2008 Chin. Phys. B 17 4080
[31]	Krsti'c M, Kanellakopoulos I and Kokotovi'c P V 1995 Nonlinear and Adaptive Control Design (New York: Wiley)

Adaptive synchronization of uncertain chaotic systems via switching mechanism

Adaptive synchronization of uncertain chaotic systems via switching mechanism

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 31

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Xiaoming Liang(梁晓明), Chao Fang(方超), Xiyun Zhang(张希昀), and Huaping Lü(吕华平). Influence of coupling asymmetry on signal amplification in a three-node motif[J]. 中国物理B, 2023, 32(1): 10504-010504.
[2]	Yong-Bing Hu(胡永兵), Xiao-Min Yang(杨晓敏), Da-Wei Ding(丁大为), and Zong-Li Yang(杨宗立). Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application[J]. 中国物理B, 2022, 31(11): 110501-110501.
[3]	Yun-Xu Ma(马云旭), Jia-Ning Wang(王佳宁), Zhao-Zhuo Zeng(曾钊卓), Ying-Yue Yuan(袁映月), Jin-Xia Yang(杨金霞), Hui-Bo Liu(刘慧博), Sen-Fu Zhang(张森富), Jian-Bo Wang(王建波), Chen-Dong Jin(金晨东), and Qing-Fang Liu(刘青芳). Spin transfer nano-oscillator based on synthetic antiferromagnetic skyrmion pair assisted by perpendicular fixed magnetic field[J]. 中国物理B, 2022, 31(10): 100501-100501.
[4]	Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control[J]. 中国物理B, 2022, 31(10): 100504-100504.
[5]	Tao Li(李涛), Lin Yan(严霖), and Zhigang Zheng(郑志刚). Improved functional-weight approach to oscillatory patterns in excitable networks[J]. 中国物理B, 2022, 31(9): 90502-090502.
[6]	Lei Tao(陶蕾) and Sheng-Jun Wang(王圣军). Power-law statistics of synchronous transition in inhibitory neuronal networks[J]. 中国物理B, 2022, 31(8): 80505-080505.
[7]	Xiang Ling(凌翔), Bo Hua(华博), Ning Guo(郭宁), Kong-Jin Zhu(朱孔金), Jia-Jia Chen(陈佳佳), Chao-Yun Wu(吴超云), and Qing-Yi Hao(郝庆一). Synchronization in multilayer networks through different coupling mechanisms[J]. 中国物理B, 2022, 31(4): 48901-048901.
[8]	Yahan Deng(邓雅瀚), Zhongkai Mo(莫中凯), and Hongqian Lu(陆宏谦). Robust H_∞ state estimation for a class of complex networks with dynamic event-triggered scheme against hybrid attacks[J]. 中国物理B, 2022, 31(2): 20503-020503.
[9]	Atiyeh Bayani, Sajad Jafari, and Hamed Azarnoush. Explosive synchronization: From synthetic to real-world networks[J]. 中国物理B, 2022, 31(2): 20504-020504.
[10]	Alireza Bahramian, Sajjad Shaukat Jamal, Fatemeh Parastesh, Kartikeyan Rajagopal, and Sajad Jafari. Collective behavior of cortico-thalamic circuits: Logic gates as the thalamus and a dynamical neuronal network as the cortex[J]. 中国物理B, 2022, 31(2): 28901-028901.
[11]	Dong-Jie Qian(钱冬杰). Explosive synchronization in a mobile network in the presence of a positive feedback mechanism[J]. 中国物理B, 2022, 31(1): 10503-010503.
[12]	Yan-Liang Jin(金彦亮), Run-Zhu Guo(郭润珠), Xiao-Qi Yu(于晓琪), and Li-Quan Shen(沈礼权). Explosive synchronization of multi-layer complex networks based on inter-layer star network connection[J]. 中国物理B, 2021, 30(12): 120505-120505.
[13]	Mei Li(李梅), Ruo-Xun Zhang(张若洵), and Shi-Ping Yang(杨世平). Adaptive synchronization of a class of fractional-order complex-valued chaotic neural network with time-delay[J]. 中国物理B, 2021, 30(12): 120503-120503.
[14]	Karthikeyan Rajagopal, Anitha Karthikeyan, and Balamurali Ramakrishnan. Controlling chaos and supressing chimeras in a fractional-order discrete phase-locked loop using impulse control[J]. 中国物理B, 2021, 30(12): 120512-120512.
[15]	Shun-Jie Li(李顺杰), Ya-Wen Wu(吴雅文), and Gang Zheng(郑刚). Adaptive synchronization of chaotic systems with less measurement and actuation[J]. 中国物理B, 2021, 30(10): 100503-100503.