Controlling Rucklidge chaotic system with a single controller using linear feedback and passive control methods

In this paper, the control of chaos with a single controller, which provides simplicity in implementation, is investigated in continuous time nonlinear Rucklidge system. For this purpose, a linear feedback controller and a passive controller are constructed and added to the Rucklidge chaotic system. Lyapunov function is used to realize that the controller ensures the global asymptotic stability of the system. Owing to the controller, Rucklidge chaotic system can be regulated to its equilibrium points. Numerical simulations of the proposed methods and local relay control method have been demonstrated, compared and discussed.

[1]  A. Rucklidge.  Chaos in models of double convection , 1992, Journal of Fluid Mechanics.

[2]  Radoslav Radev,et al.  Local Relay Control for a Class of Nonlinear Systems with Chaotic Behaviors , 2004, Int. J. Bifurc. Chaos.

[3]  Lequan Min,et al.  Partial generalized synchronization theorems of differential and discrete systems , 2008, Kybernetika.

[4]  A. Isidori,et al.  Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems , 1991 .

[5]  Emad E. Mahmoud,et al.  Passive control of n-dimensional chaotic complex nonlinear systems , 2013 .

[6]  E. O. Ochola,et al.  A hyperchaotic system without equilibrium , 2012 .

[7]  Wen Yu.  Passive equivalence of chaos in Lorenz system , 1999 .

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

[9]  Chongxin Liu,et al.  A new chaotic attractor , 2004 .

[10]  Ihsan Pehlivan,et al.  Chaotic oscillator design and realizationsof the Rucklidge attractor and its synchronization and masking simulations , 2010 .

[11]  Chi-Chuan Hwang,et al.  A linear continuous feedback control of Chua's circuit , 1997 .

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

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

[14]  Tian Li-xin.  Synchronization between different systems , 2005 .

[15]  L. O. Chua,et al.  The double scroll family. I: Rigorous of chaos. II: Rigorous analysis of bifurcation phenomena , 1986 .

[16]  Sundarapandian Vaidyanathan,et al.  Sliding Mode Controller Design for The Global Chaos Synchronization of Rucklidge Chaotic Systems , 2012 .

[17]  Bing Li,et al.  A New Four-Scroll Chaotic Attractor Consisted of Two-Scroll Transient Chaotic and Two-Scroll Ultimate Chaotic , 2012 .

[18]  Xingyuan Wang,et al.  Impulsive control and synchronization of a new unified hyperchaotic system with varying control gains and impulsive intervals , 2012 .

[19]  Li-Wei Ko,et al.  Adaptive synchronization of chaotic systems with unknown parameters via new backstepping strategy , 2012, Nonlinear Dynamics.

[20]  Miao Yu,et al.  Synchronization between uncertain chaotic systems with a diverse structure based on a second-order sliding mode control , 2012 .

[21]  Tianshou Zhou,et al.  THREE SCHEMES TO SYNCHRONIZE CHAOTIC FRACTIONAL-ORDER RUCKLIDGE SYSTEMS , 2007 .

[22]  A. N. Njah,et al.  Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques , 2010 .

[23]  Xingyuan Wang,et al.  CONTROLLING LIU SYSTEM WITH DIFFERENT METHODS , 2009 .

[24]  M. C. Lombardo,et al.  Global linear feedback control for the generalized Lorenz system , 2006 .

[25]  Xuerong Shi,et al.  A single adaptive controller with one variable for synchronizing two identical time delay hyperchaotic Lorenz systems with mismatched parameters , 2012 .

[26]  Runfan Zhang,et al.  Control of a class of fractional-order chaotic systems via sliding mode , 2012 .

[27]  Lu Jun-An,et al.  Passive control and synchronization of hyperchaotic Chen system , 2008 .

[28]  Yi Zhang,et al.  Synchronization of chaotic system and its application in secure communication , 2010, 2010 International Conference on Computer Application and System Modeling (ICCASM 2010).

[29]  L. Chua,et al.  The double scroll family , 1986 .

[30]  M. M. El-Dessoky,et al.  Controlling chaotic behaviour for spin generator and Rossler dynamical systems with feedback control , 2001 .

[31]  Alvarez-Ramírez.  Nonlinear feedback for controlling the Lorenz equation. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Chongxin Liu,et al.  Passive control on a unified chaotic system , 2010 .

[33]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[34]  Lin Shi,et al.  Analysis and control of a hyperchaotic system with only one nonlinear term , 2012 .

[35]  Leonardo Acho,et al.  Impulsive Synchronization for a New Chaotic oscillator , 2007, Int. J. Bifurc. Chaos.

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

[37]  Malek Benslama,et al.  PASSIVITY-BASED CONTROL OF CHAOTIC L ¨ US YSTEM , 2006 .

[38]  Guanrong Chen,et al.  The compound structure of a new chaotic attractor , 2002 .

[39]  Weihua Jiang,et al.  Delayed feedback control and bifurcation analysis of Rossler chaotic system , 2010 .

[40]  Chen Guan-Rong,et al.  Chaos synchronization of Rikitake chaotic attractor using the passive control technique , 2008 .

[41]  M. Paskota.  On Local Control of Chaos: the Neighbourhood Size , 1996 .

[42]  Yao Hong-xing.  Synchronization of Rucklidge system and its application in secure communication , 2006 .

[43]  Keisuke Ito,et al.  Chaos in the Rikitake two-disc dynamo system , 1980 .

[44]  Safieddine Bouali,et al.  A novel strange attractor with a stretched loop , 2012 .

[45]  Juebang Yu,et al.  Chaos synchronization using single variable feedback based on backstepping method , 2004 .

[46]  Ahmed El Hajjaji,et al.  Improved fuzzy sliding mode control for a class of MIMO nonlinear uncertain and perturbed systems , 2011, Appl. Soft Comput..

[47]  Jinhu Lu,et al.  Controlling uncertain Lü system using linear feedback , 2003 .