Robust finite-time global synchronization of chaotic systems with different orders

Abstract This article proves that the robust finite-time synchronization behavior can be achieved for the chaotic systems with different orders. Based on the Lyapunov stability theory and using the nonlinear feedback control, sufficient algebraic conditions are derived to compute the linear controller gains. These gains are then used to achieve the robust finite time increasing order and reduced order synchronization of the chaotic systems. This study also discusses the design of a controller that accomplishes the finite time synchronization of two chaotic systems of different dimensions under the effect of both unknown model uncertainties and external disturbances. Numerical simulation results are furnished to validate the theoretical findings.

[1]  Mohammad Shahzad,et al.  Global chaos synchronization of new chaotic system using linear active control , 2015, Complex..

[2]  Honglan Zhu,et al.  Anti-Synchronization of two Different Chaotic Systems via Optimal Control with Fully Unknown Parameters * , 2010 .

[3]  K. S. Ojo,et al.  Generalized reduced-order hybrid combination synchronization of three Josephson junctions via backstepping technique , 2014 .

[4]  Wuquan Li,et al.  Finite-time generalized synchronization of chaotic systems with different order , 2011 .

[5]  Alexander N. Pisarchik,et al.  Synchronization of Shilnikov chaos in a CO2 laser with feedback , 2001 .

[6]  Guanrong Chen,et al.  A new hyperchaotic Lorenz‐type system: Generation, analysis, and implementation , 2011, Int. J. Circuit Theory Appl..

[7]  Shu Fan Lim,et al.  A simple digital DCM control scheme for boost PFC operating in both CCM and DCM , 2010, 2010 IEEE Energy Conversion Congress and Exposition.

[8]  Enno de Lange,et al.  Synchronization of early afterdepolarizations and arrhythmogenesis in heterogeneous cardiac tissue models. , 2012, Biophysical journal.

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

[10]  Shuzhi Sam Ge,et al.  Synchronization of Two uncertain Chaotic Systems via Adaptive backstepping , 2001, Int. J. Bifurc. Chaos.

[11]  Yao-Chen Hung,et al.  Synchronization of Uncertain hyperchaotic and Chaotic Systems by Adaptive Control , 2008, Int. J. Bifurc. Chaos.

[12]  U. Vincent,et al.  Finite-time synchronization for a class of chaotic and hyperchaotic systems via adaptive feedback controller , 2011 .

[13]  Wei Zhang,et al.  Finite-time chaos synchronization of unified chaotic system with uncertain parameters , 2009 .

[14]  Cheng-Hsiung Yang,et al.  Generalized Synchronization with Uncertain Parameters of Nonlinear Dynamic System via Adaptive Control , 2014, TheScientificWorldJournal.

[15]  Wenwu Yu,et al.  Successive lag synchronization on nonlinear dynamical networks via linear feedback control , 2015 .

[16]  Pagavathigounder Balasubramaniam,et al.  Synchronization of chaotic systems using feedback controller: An application to Diffie–Hellman key exchange protocol and ElGamal public key cryptosystem , 2014 .

[17]  Wei Zhang,et al.  Finite-time synchronization of uncertain unified chaotic systems based on CLF☆ , 2009 .

[18]  Mohd. Salmi Md. Noorani,et al.  Adaptive Increasing-Order Synchronization and Anti-Synchronization of Chaotic Systems with Uncertain Parameters , 2011 .

[19]  S. Bowong.  Stability analysis for the synchronization of chaotic systems with different order: application to secure communications , 2004 .

[20]  Qing-Long Han,et al.  Master-slave synchronization criteria for chaotic hindmarsh-rose neurons using linear feedback control , 2016, Complex..

[21]  T. Aldemir,et al.  Synchronization of different chaotic systems using generalized active control , 2009, 2009 International Conference on Electrical and Electronics Engineering - ELECO 2009.

[22]  Lilian Huang,et al.  Synchronization of chaotic systems via nonlinear control , 2004 .

[23]  Samuel Bowong,et al.  Robust Synchronization of a Class of Nonlinear Systems: Applications to Chaotic Coupled Electromechanical Systems , 2008 .

[24]  Ki-Ryong Kwon,et al.  Perceptual encryption with compression for secure vector map data processing , 2014, Digit. Signal Process..

[25]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

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

[27]  R. Femat,et al.  Synchronization of chaotic systems with different order. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Mohammad Shahzad,et al.  A Research on the Synchronization of Two Novel Chaotic Systems Based on a Nonlinear Active Control Algorithm , 2014 .

[29]  张超,et al.  Synchronization between two different chaotic systems with nonlinear feedback control , 2007 .

[30]  X. Guowei,et al.  Synchronization of Lorenz System Based on Fast Stabilization Sliding Mode Control , 2015 .

[31]  Sonia Hammami,et al.  State feedback-based secure image cryptosystem using hyperchaotic synchronization. , 2015, ISA transactions.

[32]  Anita C. Faul,et al.  Non-linear systems , 2006 .

[33]  L. Chua,et al.  Absolute Stability Theory and the Synchronization Problem , 1997 .

[34]  Ming-Chung Ho,et al.  Reduced-order synchronization of chaotic systems with parameters unknown , 2006 .