Finite-time generalized synchronization of nonidentical delayed chaotic systems

Abstract. This paper deals with the finite-time generalized synchronization (GS) problem of driveresponse systems. The main purpose of this paper is to design suitable controllers to force the drive-response systems to realize GS in a finite time. Based on the finite-time stability theory and nonlinear control theory, sufficient conditions are derived that guarantee finite-time GS. This paper extends some basic results from generalized synchronization to delayed systems. Because finitetime GS means the optimality in convergence time and has better robustness, the results in this paper are important. Numerical examples are given to show the effectiveness of the proposed control techniques.

[1]  O. Rössler.  An equation for continuous chaos , 1976 .

[2]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[3]  Parlitz,et al.  Generalized synchronization, predictability, and equivalence of unidirectionally coupled dynamical systems. , 1996, Physical review letters.

[4]  H. Abarbanel,et al.  Generalized synchronization of chaos: The auxiliary system approach. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[5]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

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

[7]  A. Lozowski,et al.  Synchronization and anti-synchronization of Chua's oscillators via a piecewise linear coupling circuit , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

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

[9]  C. Masoller.  Anticipation in the synchronization of chaotic semiconductor lasers with optical feedback. , 2001, Physical review letters.

[10]  Daolin Xu,et al.  Controlled Projective Synchronization in Nonpartially-Linear Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[11]  Hongtao Lu.  Chaotic attractors in delayed neural networks , 2002 .

[12]  Yiguang Hong,et al.  Finite-time stabilization and stabilizability of a class of controllable systems , 2002, Syst. Control. Lett..

[13]  K. Shore,et al.  Lag times and parameter mismatches in synchronization of unidirectionally coupled chaotic external cavity semiconductor lasers. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Chuandong Li,et al.  Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication , 2004 .

[15]  Guanrong Chen,et al.  Global Synchronization of Coupled Delayed Neural Networks and Applications to Chaotic CNN Models , 2004, Int. J. Bifurc. Chaos.

[16]  Wei Lin,et al.  Global finite-time stabilization of a class of uncertain nonlinear systems , 2005, Autom..

[17]  Ned J Corron,et al.  Lag and anticipating synchronization without time-delay coupling. , 2005, Chaos.

[18]  Jamal Daafouz,et al.  Adaptive synchronization of uncertain chaotic colpitts oscillators based on parameter identification , 2005 .

[19]  Zheng Xue-mei.  Finite time synchronization of chaotic systems with unmatched uncertainties , 2006 .

[20]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[21]  Tianping Chen,et al.  Robust synchronization of delayed neural networks based on adaptive control and parameters identification , 2006 .

[22]  Jinde Cao,et al.  Adaptive synchronization and lag synchronization of uncertain dynamical system with time delay based on parameter identification , 2007 .

[23]  Ruihong Li,et al.  Synchronization of two different chaotic systems with unknown parameters , 2007 .

[24]  Yao-Chen Hung,et al.  Paths to globally generalized synchronization in scale-free networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Xiaofeng Hu,et al.  A novel definition of generalized synchronization on networks and a numerical simulation example , 2008, Comput. Math. Appl..

[26]  Chuandong Li,et al.  Synchronization of chaotic systems with delay using intermittent linear state feedback. , 2008, Chaos.

[27]  Li Liu,et al.  Finite-time stability of linear time-varying singular systems with impulsive effects , 2008, Int. J. Control.

[28]  Yongqing Yang,et al.  The impulsive control synchronization of the drive-response complex system☆ , 2008 .

[29]  Wang Xingyuan,et al.  Generalized synchronization via nonlinear control. , 2008, Chaos.

[30]  Ligang Wu,et al.  Exponential stabilization of switched stochastic dynamical networks , 2009 .

[31]  Jinde Cao,et al.  On periodic solutions of neural networks via differential inclusions , 2009, Neural Networks.

[32]  Tingwen Huang,et al.  Anticipating synchronization of a class of chaotic systems. , 2009, Chaos.

[33]  Shuguang Guan,et al.  The development of generalized synchronization on complex networks. , 2008, Chaos.

[34]  Jinde Cao,et al.  Anti-synchronization of stochastic perturbed delayed chaotic neural networks , 2009, Neural Computing and Applications.

[35]  Wei Xing Zheng,et al.  Generalized synchronization of complex dynamical networks via impulsive control. , 2009, Chaos.

[36]  Jinde Cao,et al.  Generalized synchronization of chaotic systems: an auxiliary system approach via matrix measure. , 2009, Chaos.

[37]  Lu Jinhu.  FINITE TIME SYNCHRONIZATION OF COMPLEX DYNAMICAL NETWORKS , 2009 .

[38]  Francesco Amato,et al.  Finite-time control of discrete-time linear systems: Analysis and design conditions , 2010, Autom..

[39]  Jinde Cao,et al.  Finite-time stochastic synchronization of complex networks , 2010 .

[40]  Jinde Cao,et al.  Robust State Estimation for Neural Networks With Discontinuous Activations , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[41]  Long Wang,et al.  Finite-Time Consensus Problems for Networks of Dynamic Agents , 2007, IEEE Transactions on Automatic Control.

[42]  Jinde Cao,et al.  Local synchronization of one-to-one coupled neural networks with discontinuous activations , 2011, Cognitive Neurodynamics.

[43]  Jitao Sun,et al.  Finite-time stability of linear time-varying singular impulsive systems [Brief Paper] , 2010 .

[44]  Yucai Dong,et al.  Finite Time Synchronization between Two Different Chaotic Systems with Uncertain Parameters , 2010, Comput. Inf. Sci..

[45]  Jinde Cao,et al.  Filippov systems and quasi-synchronization control for switched networks. , 2012, Chaos.

[46]  Jinde Cao,et al.  Finite-time stochastic stabilization for BAM neural networks with uncertainties , 2013, J. Frankl. Inst..

[47]  Bin Wang,et al.  Finite-time parameter identification and adaptive synchronization between two chaotic neural networks , 2013, J. Frankl. Inst..

[48]  Lihong Huang,et al.  Finite time stability of periodic solution for Hopfield neural networks with discontinuous activations , 2013, Neurocomputing.

[49]  Fei Liu,et al.  Finite-time boundedness of uncertain time-delayed neural network with Markovian jumping parameters , 2013, Neurocomputing.

[50]  Bin Wang,et al.  Finite-time synchronization control of complex dynamical networks with time delay , 2013, Commun. Nonlinear Sci. Numer. Simul..

[51]  Chuandong Li,et al.  Finite-time lag synchronization of delayed neural networks , 2014, Neurocomputing.

[52]  Jinde Cao,et al.  Nonsmooth finite-time stabilization of neural networks with discontinuous activations , 2014, Neural Networks.