Robust adaptive synchronization for a general class of uncertain chaotic systems with application to Chua's circuit.

The synchronization problem for a general class of uncertain chaotic systems is addressed. The underlying systems may be perturbed by unknown time-varying parameters, unstructured uncertainties, and external disturbances. Meanwhile, the time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Assuming the disturbances are L(2) signals, an adaptive control incorporated with H(∞) control technique is employed to construct a robust adaptive synchronization algorithm. Then, removing such assumption, a novel adaptive-based method is developed to achieve the goal of synchronization. In order to demonstrate the effectiveness of the proposed algorithms, such methods are applied to solve the synchronization problem of uncertain chaotic Chua's circuits.

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

[2]  Teh-Lu Liao,et al.  Adaptive control and synchronization of Lorenz systems , 1999 .

[3]  Yeong-Chan Chang.  A robust tracking control for chaotic Chua's circuits via fuzzy approach , 2001 .

[4]  Jun-an Lu,et al.  Adaptive feedback synchronization of a unified chaotic system , 2004 .

[5]  Jian-Xin Xu,et al.  A new periodic adaptive control approach for time-varying parameters with known periodicity , 2004, IEEE Transactions on Automatic Control.

[6]  Fang Tang,et al.  An adaptive active control for the modified Chua's circuit , 2005 .

[7]  Euntai Kim,et al.  Fuzzy adaptive synchronization of uncertain chaotic systems , 2005 .

[8]  H. N. Agiza,et al.  Adaptive synchronization of Chua's circuits with fully unknown parameters , 2006 .

[9]  J. Yan,et al.  Robust synchronization of unified chaotic systems via sliding mode control , 2007 .

[10]  Recai Kiliç,et al.  Experimental observations of EMI effects in autonomous Chua's chaotic circuit , 2007 .

[11]  Ju H. Park.  Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter , 2007 .

[12]  Z. Ding.  Asymptotic rejection of a class of periodic disturbances in nonlinear output-feedback systems , 2007 .

[13]  H. Yau,et al.  Chaos synchronization using fuzzy logic controller , 2008 .

[14]  M Roopaei,et al.  Synchronization of a class of chaotic systems with fully unknown parameters using adaptive sliding mode approach. , 2008, Chaos.

[15]  Yongguang Yu.  Adaptive synchronization of a unified chaotic system , 2008 .

[16]  Her-Terng Yau,et al.  Chaos synchronization of two uncertain chaotic nonlinear gyros using fuzzy sliding mode control , 2008 .

[17]  R. M. López-Gutiérrez,et al.  Experimental realization of synchronization in complex networks with Chua’s circuits like nodes , 2009 .

[18]  Mohammad Ataei,et al.  A chattering-free sliding mode control design for uncertain chaotic systems , 2009 .

[19]  Gang Feng,et al.  Output tracking and synchronization of chaotic Chua’s circuit with disturbances via model predictive regulator , 2009 .

[20]  E. E. García-Guerrero,et al.  Synchronization of Chua’s circuits with multi-scroll attractors: Application to communication , 2009 .

[21]  A. Markazi,et al.  Adaptive fuzzy sliding-mode control for multi-input multi-output chaotic systems , 2009 .

[22]  Bo Wang,et al.  On the synchronization of uncertain master–slave chaotic systems with disturbance , 2009 .

[23]  Dongkyoung Chwa,et al.  Synchronization of the bidirectionally coupled unified chaotic system via sum of squares method. , 2011, Chaos.