Finite-time combination-combination synchronization of four different chaotic systems with unknown parameters via sliding mode control

In this paper, we apply the nonsingular terminal sliding mode control technique to realize the novel combination-combination synchronization between combination of two chaotic systems as drive system and combination of two chaotic systems as response system with unknown parameters in a finite time. On the basic of the adaptive laws and finite-time stability theory, an adaptive combination sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time for four different chaotic systems. In theory, it is proved that the sliding mode technique can realize fast convergence for four different chaotic systems in the finite time. Some criteria and corollaries are derived for finite-time combination-combination synchronization of four different chaotic systems. Numerical simulation results are shown to verify the effectiveness and correctness of the combination-combination synchronization.

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

[2]  C. K. Michael Tse,et al.  Adaptive Feedback Synchronization of a General Complex Dynamical Network With Delayed Nodes , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[3]  Wei Zhang,et al.  Finite-time chaos control via nonsingular terminal sliding mode control , 2009 .

[4]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[5]  S. K. Dana,et al.  Design of coupling for synchronization in time-delayed systems. , 2011, Chaos.

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

[7]  Huaguang Zhang,et al.  Adaptive Synchronization Between Two Different Chaotic Neural Networks With Time Delay , 2007, IEEE Transactions on Neural Networks.

[8]  Moez Feki,et al.  Sliding mode control and synchronization of chaotic systems with parametric uncertainties , 2009 .

[9]  Tianping Chen,et al.  Partial synchronization in linearly and symmetrically coupled ordinary differential systems , 2009 .

[10]  Jun-an Lu,et al.  Using sampled-data feedback control and linear feedback synchronization in a new hyperchaotic system , 2008 .

[11]  Faqiang Wang,et al.  Synchronization of unified chaotic system based on passive control , 2007 .

[12]  Darong Lai,et al.  Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes , 2012 .

[13]  Yi Shen,et al.  General hybrid projective complete dislocated synchronization with non-derivative and derivative coupling based on parameter identification in several chaotic and hyperchaotic systems , 2013 .

[14]  M. P. Aghababa,et al.  Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique , 2011 .

[15]  L. Chua,et al.  Generalized synchronization of chaos via linear transformations , 1999 .

[16]  Yi Shen,et al.  Compound synchronization of four memristor chaotic oscillator systems and secure communication. , 2013, Chaos.

[17]  Jinde Cao,et al.  Synchronization and anti-synchronization for chaotic systems , 2007 .

[18]  Meng Liu,et al.  Adaptive projective synchronization of dynamical networks with distributed time delays , 2012 .

[19]  Dong Sun.  Position synchronization of multiple motion axes with adaptive coupling control , 2003, Autom..

[20]  Xinghuo Yu,et al.  Fast terminal sliding-mode control design for nonlinear dynamical systems , 2002 .

[21]  Luo Runzi,et al.  Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication. , 2012, Chaos.

[22]  H. Adeli,et al.  Visibility graph similarity: A new measure of generalized synchronization in coupled dynamic systems , 2012 .

[23]  A. Hramov,et al.  Time scale synchronization of chaotic oscillators , 2005, nlin/0602053.

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

[25]  Luo Runzi,et al.  Combination synchronization of three classic chaotic systems using active backstepping design. , 2011, Chaos.

[26]  Hadi Taghvafard,et al.  Phase and anti-phase synchronization of fractional order chaotic systems via active control , 2011 .

[27]  Guangzhao Cui,et al.  Combination–combination synchronization among four identical or different chaotic systems , 2013 .

[28]  Xiangjun Wu,et al.  Generalized projective synchronization of the fractional-order Chen hyperchaotic system , 2009 .

[29]  Zijiang Yang,et al.  Lag Synchronization of Unknown Chaotic Delayed Yang–Yang-Type Fuzzy Neural Networks With Noise Perturbation Based on Adaptive Control and Parameter Identification , 2009, IEEE Transactions on Neural Networks.

[30]  Ta-lun Yang,et al.  Breaking chaotic switching using generalized synchronization: examples , 1998 .

[31]  Junwei Sun,et al.  Transmission projective synchronization of multi-systems with non-delayed and delayed coupling via impulsive control. , 2012, Chaos.

[32]  P. K. Roy,et al.  Design of coupling for synchronization of chaotic oscillators. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Keiji Konishi,et al.  Sliding mode control for a class of chaotic systems , 1998 .

[34]  Xin-Chu Fu,et al.  Projective Synchronization of Driving–Response Systems and Its Application to Secure Communication , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[35]  Cheng-Hsiung Yang,et al.  Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control , 2007 .

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

[37]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[38]  Ya-Fu Peng.  Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems , 2009 .

[39]  Yongguang Yu,et al.  Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design , 2011 .

[40]  M. Rosenblum,et al.  Phase synchronization in driven and coupled chaotic oscillators , 1997 .

[41]  Huaguang Zhang,et al.  Robust Global Exponential Synchronization of Uncertain Chaotic Delayed Neural Networks via Dual-Stage Impulsive Control , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).