Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller

The adaptive synchronized problem of the four-dimensional (4D) Lü hyperchaotic system performed by Elabbasy et al. (Chaos Solitons Fractals 30:1133–1142, 2006) with uncertain parameters by applying the single control input is addressed in this article. Based on the Lyapunov theorem of stability, the single-input adaptive synchronization controllers associated with the adaptive update laws of system parameters are developed to make the states of two nearly identical 4D Lü hyperchaotic systems asymptotically synchronized. Numerical studies are presented to illustrate the effectiveness of the proposed chaotic synchronization schemes.

[1]  Her-Terng Yau,et al.  Design of Extended Backstepping Sliding Mode Controller for Uncertain Chaotic Systems , 2007 .

[2]  Zhengzhi Han,et al.  Global sliding mode control and application in chaotic systems , 2009 .

[3]  Uchechukwu E. Vincent,et al.  Chaos control of 4D chaotic systems using recursive backstepping nonlinear controller , 2007 .

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

[5]  Ying-Cheng Lai,et al.  Controlling chaos , 1994 .

[6]  Zhenya Yan,et al.  Controlling hyperchaos in the new hyperchaotic Chen system , 2005, Appl. Math. Comput..

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

[8]  Servilia Oancea,et al.  Master–slave synchronization of Lorenz systems using a single controller , 2009 .

[9]  Zhi-Hong Guan,et al.  Feedback and adaptive control for the synchronization of Chen system via a single variable , 2003 .

[10]  Andrew Chi Sing Leung,et al.  Adaptive synchronization of identical chaotic and hyper-chaotic systems with uncertain parameters , 2010 .

[11]  Ming-Jyi Jang,et al.  Sliding mode control of hyperchaos in Rössler systems , 2002 .

[12]  Zuo-Lei Wang,et al.  Anti-synchronization of Liu system and Lorenz system with known or unknown parameters , 2009 .

[13]  M. T. Yassen,et al.  Adaptive control and synchronization of a modified Chua's circuit system , 2003, Appl. Math. Comput..

[14]  M. T. Yassen,et al.  Synchronization hyperchaos of hyperchaotic systems , 2008 .

[15]  Faqiang Wang,et al.  A new criterion for chaos and hyperchaos synchronization using linear feedback control , 2006 .

[16]  José Manoel Balthazar,et al.  On control and synchronization in chaotic and hyperchaotic systems via linear feedback control , 2008 .

[17]  M. M. El-Dessoky,et al.  Adaptive synchronization of a hyperchaotic system with uncertain parameter , 2006 .

[18]  Zuolei Wang.  Projective synchronization of hyperchaotic Lü system and Liu system , 2010 .

[19]  Hao Zhang,et al.  Controlling and tracking hyperchaotic Rössler system via active backstepping design , 2005 .

[20]  A. N. Njah,et al.  Generalization on the chaos control of 4-D chaotic systems using recursive backstepping nonlinear controller , 2009 .

[21]  M. T. Yassen,et al.  On hyperchaos synchronization of a hyperchaotic Lü system , 2008 .

[22]  Yi Li,et al.  Adaptive control and synchronization of a new modified hyperchaotic Lü system with uncertain parameters , 2009 .

[23]  Juhn-Horng Chen,et al.  A new hyper-chaotic system and its synchronization , 2009 .

[24]  Q. Jia.  Adaptive control and synchronization of a new hyperchaotic system with unknown parameters , 2007 .

[25]  Antonio Loría,et al.  A Linear Time-Varying Controller for Synchronization of LÜ Chaotic Systems With One Input , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[26]  Wei Zhang,et al.  Finite-time chaos control of unified chaotic systems with uncertain parameters , 2009 .

[27]  Uchechukwu E. Vincent,et al.  Synchronization of identical and non-identical 4-D chaotic systems using active control , 2008 .

[28]  Chao-Chung Peng,et al.  Robust chaotic control of Lorenz system by backstepping design , 2008 .

[29]  Yi Li,et al.  Adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters , 2008, Appl. Math. Comput..

[30]  Ju H. Park.  Adaptive synchronization of hyperchaotic Chen system with uncertain parameters , 2005 .

[31]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[32]  H. N. Agiza,et al.  Chaos synchronization of Lü dynamical system , 2004 .

[33]  Xuerong Shi,et al.  Bursting synchronization of Hind–Rose system based on a single controller , 2009 .