Approximate synchronization of two non-linear systems via impulsive control

In this paper, the approximate synchronization problem of two non-identical non-linear systems is investigated. Based on the impulsive control method, a sufficient condition is given to guarantee the approximate synchronization. Furthermore, the optimal impulsive interval problem is studied which can reduce the cost of impulsive controller, and the maximum impulsive interval is obtained by solving a non-linear optimization problem via a mixed algorithm combining chaos optimization and linear matrix inequality method. Two different chaotic systems and two different complex dynamical networks are presented respectively to verify the effectiveness of the proposed methods.

[1]  Wansheng Tang,et al.  Control and synchronization for a class of new chaotic systems via linear feedback , 2009 .

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

[3]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[4]  Jun-Guo Lu,et al.  Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach , 2009 .

[5]  Guanrong Chen,et al.  On a Generalized Lorenz Canonical Form of Chaotic Systems , 2002, Int. J. Bifurc. Chaos.

[6]  Jinde Cao,et al.  Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) systems with fully unknown parameters. , 2005, Chaos.

[7]  J. Aubin.  Optima and Equilibria: An Introduction to Nonlinear Analysis , 1993 .

[8]  Liang Chen,et al.  Adaptive synchronization between two complex networks with nonidentical topological structures , 2008 .

[9]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

[10]  Mohammad Saleh Tavazoei,et al.  Comparison of different one-dimensional maps as chaotic search pattern in chaos optimization algorithms , 2007, Appl. Math. Comput..

[11]  Jitao Sun,et al.  Impulsive control and synchronization of general chaotic system , 2006 .

[12]  E. M. Shahverdiev,et al.  Generalized synchronization in time-delayed systems. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  Li Bing.  The Improvement of Chaos Optimization Algorithm and the Analysis of the Property of Global Asymptotical Convergence , 2003 .

[14]  Wansheng Tang,et al.  Output feedback optimal guaranteed cost control of uncertain piecewise linear systems , 2009 .

[15]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[16]  Gao Ming,et al.  Adaptive synchronization in an array of asymmetric coupled neural networks , 2009 .

[17]  G. Butler,et al.  COMPARISON THEOREMS FOR SECOND-ORDER OPERATOR-VALUED LINEAR DIFFERENTIAL EQUATIONS , 1984 .

[18]  Z. Q. Zhu,et al.  Robust Synchronization by Time-Varying Impulsive Control , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[19]  Joaquín Míguez,et al.  An approximate gradient-descent method for joint parameter estimation and synchronization of coupled chaotic systems , 2006 .

[20]  Bing Li,et al.  Optimizing Complex Functions by Chaos Search , 1998, Cybern. Syst..

[21]  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).

[22]  Licheng Jiao,et al.  Synchronization in complex dynamical networks with nonsymmetric coupling , 2008 .

[23]  Manfeng Hu,et al.  Impulsive control of projective synchronization in chaotic systems , 2008 .

[24]  Guanrong Chen,et al.  Chaos synchronization of general complex dynamical networks , 2004 .

[25]  Maria Domenica Di Benedetto,et al.  Approximate equivalence and synchronization of metric transition systems , 2009, Syst. Control. Lett..