Robust synchronization for a class of fractional-order chaotic and hyperchaotic systems

Abstract In this paper, the issue of robust synchronization for a class of fractional-order chaotic and hyperchaotic systems with model uncertainties and disturbances is studied. A stability criterion for fractional-order nonlinear dynamic systems is introduced, and an adaptive scheme is contrived to accomplish synchronization of fractional-order chaotic and hyperchaotic systems. The controller contains only a single state variable, which is simple and flexible in implementation. Two corresponding numerical examples are given to confirm the theoretical results of the paper.

[1]  Yongguang Yu.  Adaptive synchronization of a unified chaotic system , 2008 .

[2]  N. Ford,et al.  Analysis of Fractional Differential Equations , 2002 .

[3]  M. Caputo.  Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[4]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[5]  Mohd. Salmi Md. Noorani,et al.  Homotopy analysis method for solving fractional Lorenz system , 2010 .

[6]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .

[7]  B. Mandelbrot.  Fractal Geometry of Nature , 1984 .

[8]  Hadi Taghvafard,et al.  Phase and anti-phase synchronization of fractional order chaotic systems via active control , 2011 .

[9]  Kehui Sun,et al.  Chaos synchronization between two different fractional-order hyperchaotic systems , 2011 .

[10]  Sohrab Khanmohammadi,et al.  Synchronization of two different uncertain chaotic systems with unknown parameters using a robust adaptive sliding mode controller , 2011 .

[11]  R. Magin,et al.  Fractional calculus in viscoelasticity: An experimental study , 2010 .

[12]  Shangbo Zhou,et al.  Chaos synchronization of the fractional-order Chen's system , 2009 .

[13]  Jian-An Fang,et al.  Synchronization of N-coupled fractional-order chaotic systems with ring connection , 2010 .

[14]  Hongtao Lu,et al.  Synchronization of a new fractional-order hyperchaotic system , 2009 .

[15]  W. Deng,et al.  Chaos synchronization of the fractional Lü system , 2005 .

[16]  I. Podlubny.  Fractional differential equations , 1998 .

[17]  P. Arena,et al.  Nonlinear Noninteger Order Circuits and Systems — An Introduction , 2000 .

[18]  P. Butzer,et al.  AN INTRODUCTION TO FRACTIONAL CALCULUS , 2000 .

[19]  Baogui Xin,et al.  Projective synchronization of chaotic fractional-order energy resources demand–supply systems via linear control , 2011 .

[20]  Mohammad Pourmahmood Aghababa,et al.  A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs , 2011 .

[21]  E. Ahmed,et al.  On fractional order differential equations model for nonlocal epidemics , 2007, Physica A: Statistical Mechanics and its Applications.

[22]  Naser Pariz,et al.  A chaotic secure communication scheme using fractional chaotic systems based on an extended fractional Kalman filter , 2009 .

[23]  M. Haeri,et al.  Synchronization of chaotic fractional-order systems via active sliding mode controller , 2008 .

[24]  Weihua Deng,et al.  CHAOS SYNCHRONIZATION OF FRACTIONAL-ORDER DIFFERENTIAL SYSTEMS , 2006 .

[25]  Chun-Lai Li,et al.  Tracking control and generalized projective synchronization of a class of hyperchaotic system with unknown parameter and disturbance , 2012 .