ADAPTIVE CONTROL AND SYNCHRONIZATION OF THE CAI SYSTEM

This paper derives new results for the adaptive control and synchronization design of the Cai system (2007), when the system parameters are unknown. Cai system is one of the paradigms of 3-D chaotic systems discovered by Cai and Tan (2007). In this paper, we first construct an adaptive controller to stabilize the Cai system to its unstable equilibrium at the origin. Then we build an adaptive synchronizer to achieve global chaos synchronization of the identical Cai systems with unknown parameters. The results derived for adaptive stabilization and adaptive synchronization for the Cai systems have been established using adaptive control theory and Lyapunov stability theory. Numerical simulations have been shown to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper for the Cai system.

[1]  S. M. Lee,et al.  Adaptive synchronization of Genesio-Tesi chaotic system via a novel feedback control , 2007 .

[2]  R. Tang,et al.  An extended active control for chaos synchronization , 2009 .

[3]  Bernd Blasius,et al.  Complex dynamics and phase synchronization in spatially extended ecological systems , 1999, Nature.

[4]  Teh-Lu Liao,et al.  Adaptive synchronization of chaotic systems and its application to secure communications , 2000 .

[5]  Sundarapandian Vaidyanathan,et al.  ADAPTIVE CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC CHEN SYSTEM , 2011 .

[6]  Yao-Chen Hung,et al.  Synchronization of two different systems by using generalized active control , 2002 .

[7]  Ju H. Park,et al.  A novel criterion for delayed feedback control of time-delay chaotic systems , 2005 .

[8]  Morton Nadler,et al.  The stability of motion , 1961 .

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

[10]  V. Sundarapandian,et al.  Global Chaos Synchronization of Lorenz and Pehlivan Chaotic Systems by Nonlinear Control , 2011 .

[11]  Wei Xu,et al.  Synchronization of two chaotic nonlinear gyros using active control , 2005 .

[12]  Tao Yang Control of Chaos Using Sampled-Data Feedback Control , 1998 .

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

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

[15]  Lixin Tian,et al.  Feedback control and adaptive control of the energy resource chaotic system , 2007 .

[16]  M. Feki An adaptive chaos synchronization scheme applied to secure communication , 2003 .

[17]  Y. Kuramoto,et al.  Dephasing and bursting in coupled neural oscillators. , 1995, Physical review letters.

[18]  M. Lakshmanan,et al.  Chaos in Nonlinear Oscillators: Controlling and Synchronization , 1996 .

[19]  Guoliang Cai,et al.  Chaos Synchronization of a New Chaotic System via Nonlinear Control , 2007 .

[20]  Lixin Tian,et al.  Adaptive Control and Slow Manifold Analysis of a New Chaotic System , 2006 .

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

[22]  K.Murali,et al.  Secure communication using a compound signal from generalized synchronizable chaotic systems , 1997, chao-dyn/9709025.

[23]  O. Rössler An equation for continuous chaos , 1976 .

[24]  Keiji Konishi,et al.  Sliding mode control for a class of chaotic systems , 1998 .

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