Robust adaptive backstepping synchronization for a class of uncertain chaotic systems using fuzzy disturbance observer

This paper proposes a robust adaptive backstepping synchronization method for a class of uncertain chaotic systems. Unknown factors including system uncertainties and external disturbances are estimated by a fuzzy disturbance observer. By use of the fuzzy disturbance observer, any prior information about the unknown factors is not need. The proposed method using the estimated values guarantees the global synchronization for chaotic systems with mismatched uncertainties in the sense of uniform ultimate boundedness. Finally, numerical examples are presented to show the effectiveness of the method.

[1]  Her-Terng Yau,et al.  Chaos synchronization of different chaotic systems subjected to input nonlinearity , 2008, Appl. Math. Comput..

[2]  Euntai Kim,et al.  A fuzzy disturbance observer and its application to control , 2002, IEEE Trans. Fuzzy Syst..

[3]  Juebang Yu,et al.  Chaos synchronization using single variable feedback based on backstepping method , 2004 .

[4]  Euntai Kim,et al.  Fuzzy disturbance observer approach to robust tracking control of nonlinear sampled systems with the guaranteed suboptimal H/sub /spl infin// performance , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Guo-Ping Jiang,et al.  A New Criterion for Chaos Synchronization Using Linear State Feedback Control , 2003, Int. J. Bifurc. Chaos.

[6]  Da Lin,et al.  Dynamic fuzzy neural networks modeling and adaptive backstepping tracking control of uncertain chaotic systems , 2010, Neurocomputing.

[7]  Tzuyin Wu,et al.  Chaos control of the modified Chua's circuit system , 2002 .

[8]  Jiang Wang,et al.  Feedback linearization control of chaos synchronization in coupled map-based neurons under external electrical stimulation , 2011 .

[9]  Yi-You Hou,et al.  Reliable synchronization of nonlinear chaotic systems , 2009, Math. Comput. Simul..

[10]  D. H. Ji,et al.  ' s personal copy H 1 synchronization of time-delayed chaotic systems , 2008 .

[11]  Wei Zhang,et al.  Sliding mode control for chaotic systems based on LMI , 2009 .

[12]  D. H. Ji,et al.  Synchronization of neutral complex dynamical networks with coupling time-varying delays , 2011 .

[13]  P. Olver.  Nonlinear Systems , 2013 .

[14]  Reza Shahnazi,et al.  Synchronization of general chaotic systems using neural controllers with application to secure communication , 2011, Neural Computing and Applications.

[15]  Samuel Bowong,et al.  Adaptive synchronization of chaotic systems with unknown bounded uncertainties via backstepping approach , 2007 .

[16]  Wang Xing-Yuan.  Robust Anti-synchronization of a Class of Delayed Chaotic Neural Networks , 2008 .

[17]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[18]  S. Ge,et al.  Adaptive synchronization of uncertain chaotic systems via backstepping design , 2001 .

[19]  Jiang Bin,et al.  Sliding mode synchronization controller design with neural network for uncertain chaotic systems , 2009 .

[20]  Lilian Huang,et al.  Parameters identification and adaptive synchronization of chaotic systems with unknown parameters , 2005 .

[21]  M. Feki.  An adaptive chaos synchronization scheme applied to secure communication , 2003 .

[22]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[23]  H Henk Nijmeijer,et al.  Synchronization of Mechanical Systems , 2003 .

[24]  A. Edwards,et al.  Sync-how order emerges from chaos in the universe, nature, and daily life , 2005 .

[25]  S. M. Lee,et al.  Synchronization for chaotic Lur’e systems with sector-restricted nonlinearities via delayed feedback control , 2009 .

[26]  D. Ji,et al.  Synchronization of two different non-autonomous chaotic systems using fuzzy disturbance observer , 2010 .

[27]  Sung Tae Jung,et al.  Adaptive H∞ synchronization for uncertain chaotic systems with external disturbance , 2010 .

[28]  José Manoel Balthazar,et al.  Synchronization of the unified chaotic system and application in secure communication , 2009 .

[29]  Wei-Jie Sun.  A global asymptotic synchronization problem via internal model approach , 2010 .

[30]  Li-Xin Wang,et al.  A Course In Fuzzy Systems and Control , 1996 .

[31]  H. Salarieh,et al.  Adaptive synchronization of two chaotic systems with stochastic unknown parameters , 2009 .

[32]  Gang Hu,et al.  Synchronization of a one-dimensional array of Chua's circuits by feedback control and noise , 1995 .

[33]  Leon O. Chua,et al.  Secure communication via chaotic parameter modulation , 1996 .