Singular reduced-order observer-based synchronization for uncertain chaotic systems subject to channel disturbance and chaos-based secure communication

This paper deals with the issues of chaotic synchronization and chaos-based secure communication for chaotic systems subject to uncertain parameters and channel disturbance. First, an augmented singular system is constructed by introducing an augmented vector which consists of both the state and channel disturbance vectors of original drive system, and a singular reduced-order observer which can not only synchronize the drive system but also reconstruct channel disturbance is developed for the augmented singular system. Second, a second-order sliding mode observer is considered to get the exact estimates of output derivatives in a finite time. Based on the estimates of states and output derivatives, a kind of algebraic unknown information recovery method which can recover information signal injected into the drive system and estimate parameter disturbance is proposed. Finally, a numerical simulation example is given to illustrate the effectiveness of the proposed methods.

[1]  Yi Li,et al.  Adaptive control and synchronization of a novel hyperchaotic system with uncertain parameters , 2008, Appl. Math. Comput..

[2]  Jun Ma,et al.  Optimize design of adaptive synchronization controllers and parameter observers in different hyperchaotic systems , 2010, Appl. Math. Comput..

[3]  Jinde Cao,et al.  Synchronization of switched system and application in communication , 2008 .

[4]  Chi-Ching Yang,et al.  One input control of exponential synchronization for a four-dimensional chaotic system , 2013, Appl. Math. Comput..

[5]  Ju H. Park,et al.  H∞ synchronization of chaotic systems via dynamic feedback approach , 2008 .

[6]  Haibo Jiang,et al.  Impulsive generalized synchronization for a class of nonlinear discrete chaotic systems , 2011 .

[7]  Robin J. Evans,et al.  Adaptive Observer-Based Synchronization of Chaotic Systems With First-Order Coder in the Presence of Information Constraints , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[8]  Ju H. Park,et al.  Adaptive synchronization for uncertain chaotic neural networks with mixed time delays using fuzzy disturbance observer , 2013, Appl. Math. Comput..

[9]  Wei Ding,et al.  Impulsive synchronization for a chaotic system with channel time-delay , 2011 .

[10]  M. P. Aghababa,et al.  Design of a sliding mode controller for synchronizing chaotic systems with parameter and model uncertainties and external disturbances , 2012 .

[11]  Junqi Yang,et al.  Synchronization for chaotic systems and chaos-based secure communications via both reduced-order and step-by-step sliding mode observers , 2013, Commun. Nonlinear Sci. Numer. Simul..

[12]  Ju H. Park,et al.  Robust adaptive backstepping synchronization for a class of uncertain chaotic systems using fuzzy disturbance observer , 2012 .

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

[14]  Jinde Cao,et al.  Adaptive Stabilization and Synchronization for Chaotic Lur'e Systems With Time-Varying Delay , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Song Zheng,et al.  Adaptive modified function projective synchronization of unknown chaotic systems with different order , 2012, Appl. Math. Comput..

[16]  Guanrong Chen,et al.  Secure synchronization of a class of chaotic systems from a nonlinear observer approach , 2005, IEEE Transactions on Automatic Control.

[17]  Ju H. Park.  A note on synchronization between two different chaotic systems , 2009 .

[18]  Yuanwei Jing,et al.  Modified projective synchronization of chaotic systems with disturbances via active sliding mode control , 2010 .

[19]  Jinde Cao,et al.  Impulsive synchronization of two nonidentical chaotic systems with time-varying delay , 2011 .

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

[21]  Martin J. Corless,et al.  State and Input Estimation for a Class of Uncertain Systems , 1998, Autom..

[22]  Jian Xu,et al.  The Combination of High-Gain Sliding Mode Observers Used as Receivers in Secure Communication , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[23]  Sung Tae Jung,et al.  Adaptive H∞ synchronization for uncertain chaotic systems with external disturbance , 2010 .

[24]  Li-Peng Wang,et al.  Lag synchronization of chaotic systems with parameter mismatches , 2011 .

[25]  Shou-Wei Gao,et al.  Singular observer approach for chaotic synchronization and private communication , 2011 .

[26]  Congxu Zhu,et al.  Adaptive synchronization of two novel different hyperchaotic systems with partly uncertain parameters , 2009, Appl. Math. Comput..

[27]  Le Hoa Nguyen,et al.  Adaptive synchronization of two coupled chaotic Hindmarsh-Rose neurons by controlling the membrane potential of a slave neuron , 2013 .

[28]  Henk Nijmeijer,et al.  An observer looks at synchronization , 1997 .

[29]  Jiang-Wen Xiao,et al.  Adaptive control and synchronization for chaotic systems with parametric uncertainties , 2008 .

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

[31]  Arie Levant,et al.  Higher-order sliding modes, differentiation and output-feedback control , 2003 .

[32]  Chao-Jung Cheng,et al.  Robust synchronization of uncertain unified chaotic systems subject to noise and its application to secure communication , 2012, Appl. Math. Comput..

[33]  Zhen Wang,et al.  Reduced-order observer design for the synchronization of the generalized Lorenz chaotic systems , 2012, Appl. Math. Comput..

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

[35]  Ali Abdullah,et al.  Synchronization and secure communication of uncertain chaotic systems based on full-order and reduced-order output-affine observers , 2013, Appl. Math. Comput..

[36]  Hamid Reza Karimi,et al.  Robust H∞ synchronization of a hyper-chaotic system with disturbance input , 2013 .

[37]  Mao-Yin Chen,et al.  Unknown input observer based chaotic secure communication , 2008 .