Globally Stable Synchronization of Chaotic Systems Based on Norm Observers Connected in Cascade

The synchronization of chaotic systems is achieved using output-feedback sliding mode control even in the presence of disturbances. Norm observers connected in cascade estimate upper bounds of the state variables required for the realization of the control law. This approach allows the proof of global stability and exponential convergence of the state errors based on Lyapunov's stability theory and input-to-state-stability properties of a broad class of chaotic systems. Thus, the global synchronization is guaranteed such that the initial conditions of the master (transmitter) and slave (receiver) systems can be arbitrary. The unified formulation of the chaotic systems with time-varying parameters allows periodic switching between Lorenz and Chen attractors. Simulation results illustrate the fast synchronization of master-slave chaotic oscillators and their application to a secure communication system using a time-varying cryptographic key and nonlinear encryption functions, which improve the privacy of the proposed scheme.

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

[2]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[3]  Antonio Loría,et al.  A Linear Time-Varying Controller for Synchronization of LÜ Chaotic Systems With One Input , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[4]  Luxi Yang,et al.  A robust digital secure communication scheme based on sporadic coupling chaos synchronization , 2000 .

[5]  Daizhan Cheng,et al.  Bridge the Gap between the Lorenz System and the Chen System , 2002, Int. J. Bifurc. Chaos.

[6]  Chongxin Liu,et al.  Hyperchaos synchronization of fractional-order arbitrary dimensional dynamical systems via modified sliding mode control , 2014 .

[7]  Yu-Ping Tian,et al.  Stabilizing periodic solutions of nonlinear systems and applications in chaos control , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[8]  Jamal Daafouz,et al.  A connection between chaotic and conventional cryptography , 2008, IEEE Transactions on Circuits and Systems I: Regular Papers.

[9]  Tao Liu,et al.  A novel three-dimensional autonomous chaos system , 2009 .

[10]  David J. Hill,et al.  Global Asymptotical Synchronization of Chaotic Lur'e Systems Using Sampled Data: A Linear Matrix Inequality Approach , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[11]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[12]  Zhong-Ping Jiang,et al.  A note on chaotic secure communication systems , 2002 .

[13]  Liu Hsu,et al.  Design of First-Order Approximation Filters for Sliding-Mode Control of Uncertain Systems , 2008, IEEE Transactions on Industrial Electronics.

[14]  Wu-Hua Chen,et al.  On Sampled-Data Control for Master-Slave Synchronization of Chaotic Lur'e Systems , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[16]  S. Boccaletti,et al.  The control of chaos: theory and applications , 2000 .

[17]  Alan V. Oppenheim,et al.  Circuit implementation of synchronized chaos with applications to communications. , 1993, Physical review letters.

[18]  Antonio Loría,et al.  Adaptive Unknown-Input Observers-Based Synchronization of Chaotic Systems for Telecommunication , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Antonio Loría.  Master–Slave Synchronization of Fourth-Order Lü Chaotic Oscillators via Linear Output Feedback , 2010, IEEE Transactions on Circuits and Systems II: Express Briefs.

[20]  Liu Hsu,et al.  Sliding Mode Control of Uncertain Multivariable Nonlinear Systems With Unknown Control Direction via Switching and Monitoring Function , 2010, IEEE Transactions on Automatic Control.

[21]  Wei Xing Zheng,et al.  Integral-observer-based chaos synchronization , 2006, IEEE Trans. Circuits Syst. II Express Briefs.

[22]  Hamid Reza Karimi,et al.  Delay-range-dependent exponential H∞ synchronization of a class of delayed neural networks , 2009 .

[23]  Zheng-Ming Ge,et al.  Chaotic ranges of a unified chaotic system and its chaos for five periodic switch cases , 2007 .

[24]  Adonis Bogris,et al.  Chaos-based communications at high bit rates using commercial fibre-optic links , 2006, SPIE/OSA/IEEE Asia Communications and Photonics.

[25]  Wallace Kit-Sang Tang,et al.  Cryptanalysis of Chaotic Masking Secure Communication Systems Using an Adaptive Observer , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[26]  Ursula Faber,et al.  Controlling Chaos Suppression Synchronization And Chaotification , 2016 .

[27]  Eduardo D. Sontag,et al.  Input-Output-to-State Stability , 2001, SIAM J. Control. Optim..

[28]  Min Wu,et al.  Improved Global Asymptotical Synchronization of Chaotic Lur'e Systems With Sampled-Data Control , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[29]  Wu Xiaoqun,et al.  A unified chaotic system with continuous periodic switch , 2004 .

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

[31]  Guo-Ping Jiang,et al.  Stabilizing unstable equilibria of chaotic systems from a State observer approach , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[32]  Victor Hugo Pereira Rodrigues,et al.  Chaos synchronization applied to secure communication via sliding mode control and norm state observers , 2014, VSS.