Synchronizing Genesio Chaotic System by Zhang-Dynamics Controller without or with Noise Perturbation

This paper investigates the synchronization control of Genesio chaotic system. For solving the synchronization problem of Genesio chaotic system, Zhang dynamics (ZD) method is firstly presented and utilized, and the corresponding ZD controller is designed and investigated for synchronizing control. On the one hand, the ZD controller for the synchronization of Genesio chaotic system without noise perturbation is considered, and the synchronization error between the drive Genesio chaotic subsystem and the response Genesio chaotic subsystem globally exponentially converges to zero. On the other hand, the ZD controller for the synchronization of Genesio chaotic system with noise perturbation is also considered, and detailed theoretical analyses show that the synchronization error globally converges to a small error bound or its inside. Note that the ZD controller provided here is not only effective but also robust for the synchronization of Genesio chaotic system. Finally, the simulations and comparisons with different methods for synchronizing Genesio chaotic system substantiate the efficacy, robustness and advantage of the presented ZD controller in the synchronization control.

[1]  Chung Choo Chung,et al.  Robust output feedback control for unknown non-linear systems with external disturbance , 2016 .

[2]  Ju H. Park.  Adaptive Synchronization of a Unified Chaotic System with an Uncertain Parameter , 2005 .

[3]  Oh-Min Kwon,et al.  LMI optimization approach to stabilization of time-delay chaotic systems , 2005 .

[4]  Chun-Lai Li,et al.  Analysis of a novel three-dimensional chaotic system , 2013 .

[5]  Weiqi Wang,et al.  Optical-feedback induced chaos and its control in semiconductor lasers based on sliding tunable dual-wedges , 2012 .

[6]  Bao-Zhu Guo,et al.  The Active Disturbance Rejection Control to Stabilization for Multi-Dimensional Wave Equation With Boundary Control Matched Disturbance , 2015, IEEE Transactions on Automatic Control.

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

[8]  Jun-an Lu,et al.  Parameter identification and backstepping control of uncertain Lü system , 2003 .

[9]  Yunong Zhang,et al.  Design and experimentation of acceleration-level drift-free scheme aided by two recurrent neural networks , 2013 .

[10]  Jimmie Gilbert,et al.  Linear Algebra and Matrix Theory , 1991 .

[11]  Shihua Chen,et al.  Synchronizing the noise-perturbed unified chaotic system by sliding mode control , 2006 .

[12]  Emre Salman,et al.  Figures-of-Merit to Evaluate the Significance of Switching Noise in Analog Circuits , 2015, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[13]  W. Rugh.  Linear System Theory , 1992 .

[14]  Mohammad Pourmahmood Aghababa,et al.  Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems , 2013, Int. J. Control.

[15]  Zhijun Zhang,et al.  Acceleration-Level Cyclic-Motion Generation of Constrained Redundant Robots Tracking Different Paths. , 2012, IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics : a publication of the IEEE Systems, Man, and Cybernetics Society.

[16]  Jing Na,et al.  Adaptive Control for Nonlinear Pure-Feedback Systems With High-Order Sliding Mode Observer , 2013, IEEE Transactions on Neural Networks and Learning Systems.

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

[18]  Yunong Zhang,et al.  Two New Types of Zhang Neural Networks Solving Systems of Time-Varying Nonlinear Inequalities , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Chung Choo Chung,et al.  High-Gain Disturbance Observer-Based Backstepping Control With Output Tracking Error Constraint for Electro-Hydraulic Systems , 2015, IEEE Transactions on Control Systems Technology.

[20]  Vincent Acary,et al.  Chattering-Free Digital Sliding-Mode Control With State Observer and Disturbance Rejection , 2012, IEEE Transactions on Automatic Control.

[21]  Li Xiao,et al.  Generalized synchronization of arbitrary-dimensional chaotic systems , 2015 .

[22]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[23]  Shuai Li,et al.  Nonlinearly Activated Neural Network for Solving Time-Varying Complex Sylvester Equation , 2014, IEEE Transactions on Cybernetics.

[24]  Yunong Zhang,et al.  Singularity-conquering tracking control of a class of chaotic systems using Zhang-gradient dynamics , 2015 .

[25]  Long Jin,et al.  Discrete-Time Zhang Neural Network for Online Time-Varying Nonlinear Optimization With Application to Manipulator Motion Generation , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[26]  M. Mossa Al-sawalha,et al.  Synchronization between different dimensional chaotic systems using two scaling matrices , 2016 .

[27]  Guanrong Chen,et al.  On some controllability conditions for chaotic dynamics control , 1997 .

[28]  Shihua Chen,et al.  Adaptive synchronization of uncertain hyperchaotic systems based on parameter identification , 2005 .

[29]  Mohammad Pourmahmood Aghababa,et al.  Design of hierarchical terminal sliding mode control scheme for fractional-order systems , 2015 .

[30]  Ju H. Park.  Synchronization of Genesio chaotic system via backstepping approach , 2006 .

[31]  Branislava Perunicic-Drazenovic,et al.  Integral Sliding Manifold Design for Linear Systems With Additive Unmatched Disturbances , 2016, IEEE Transactions on Automatic Control.

[32]  Mohammad Shahzad,et al.  The synchronization of chaotic systems with different dimensions by a robust generalized active control , 2016 .

[33]  Alberto Tesi,et al.  Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems , 1992, Autom..

[34]  Shuzhi Sam Ge,et al.  Design and analysis of a general recurrent neural network model for time-varying matrix inversion , 2005, IEEE Transactions on Neural Networks.

[35]  Hanlin He,et al.  Adaptive backstepping synchronization between chaotic systems with unknown Lipschitz constant , 2014, Appl. Math. Comput..

[36]  Junping Du,et al.  Chaotic satellite attitude control by adaptive approach , 2014, Int. J. Control.

[37]  Ju H. Park,et al.  Robust synchronisation of chaotic systems with randomly occurring uncertainties via stochastic sampled-data control , 2013, Int. J. Control.

[38]  Xinzhi Liu,et al.  Novel integral inequality approach on master–slave synchronization of chaotic delayed Lur’e systems with sampled-data feedback control , 2016 .

[39]  Long Jin,et al.  G2-Type SRMPC Scheme for Synchronous Manipulation of Two Redundant Robot Arms , 2015, IEEE Transactions on Cybernetics.