Control of multi-scroll Chen system

Abstract This paper investigates the chaos control problem of a new multi-scroll chaotic system. Two nonlinear control methods are studied, namely high-order and predictive types of control. The proposed methodologies offer the possibility of stabilizing unstable periodic orbits and unstable equilibrium points from the state equations. For this purpose, we apply the high-order control method for stabilizing a desired unstable periodic orbit, while the predictive control method is applied for stabilization problem of unstable equilibrium points. In particular, these approaches are effective and easy to be implemented since we only need to apply small perturbations to the system dynamics. The multi-scroll Chen system is used as representative example to show the working principle of these methods. Numerical simulation results indicate the potential engineering applications of the proposed control methods for various multi-scroll chaos-based practical applications.

[1]  Abdelkrim Boukabou,et al.  Generalized chaos control and synchronization by nonlinear high-order approach , 2012, Math. Comput. Simul..

[2]  Jinhu Lu,et al.  Generating multi-scroll chaotic attractors by thresholding , 2008 .

[3]  Jinhu Lu,et al.  Consensus of discrete-time multi-agent systems with transmission nonlinearity , 2013, Autom..

[4]  Marcelo A. Savi,et al.  Controlling chaos in a nonlinear pendulum using an extended time-delayed feedback control method , 2009 .

[5]  Pedro T. Monteiro,et al.  Dynamical modeling and analysis of large cellular regulatory networks. , 2013, Chaos.

[6]  Gauthier,et al.  Stabilizing unstable periodic orbits in a fast diode resonator using continuous time-delay autosynchronization. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Tamás Roska,et al.  MOS-integrable circuitry for multi-scroll chaotic grid realization: A SPICE-assisted proof , 2009 .

[8]  N. Inaba,et al.  OPF chaos control in a circuit containing a feedback voltage pulse generator , 1998 .

[9]  Daizhan Cheng,et al.  Characterizing the synchronizability of small-world dynamical networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[10]  J. Suykens,et al.  Generation of n-double scrolls (n=1, 2, 3, 4,...) , 1993 .

[11]  William L. Ditto,et al.  Removal, Suppression, and Control of Chaos by Nonlinear Design , 1995 .

[12]  Ahmed S. Elwakil,et al.  Multiscroll Chaotic Oscillators: The Nonautonomous Approach , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  Pei Yu,et al.  Chaos control and chaos synchronization for multi-scroll chaotic attractors generated using hyperbolic functions , 2010 .

[14]  Xinghuo Yu,et al.  Design and Implementation of Grid Multiwing Hyperchaotic Lorenz System Family via Switching Control and Constructing Super-Heteroclinic Loops , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

[15]  Austin Blaquière,et al.  Nonlinear System Analysis , 1966 .

[16]  Huaguang Zhang,et al.  Synchronization criteria and pinning control for complex networks with multiple delays , 2011, Neural Computing and Applications.

[17]  Jianfeng Feng,et al.  Locating unstable periodic orbits: when adaptation integrates into delayed feedback control. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  P. Arena,et al.  Generation of n-double scrolls via cellular neural networks , 1996, Int. J. Circuit Theory Appl..

[19]  Xinghuo Yu,et al.  Chaos control : theory and applications , 2003 .

[20]  E. E. García-Guerrero,et al.  Synchronization of Chua’s circuits with multi-scroll attractors: Application to communication , 2009 .

[21]  Maciej Ogorzalek,et al.  Global relative parameter sensitivities of the feed-forward loops in genetic networks , 2012, Neurocomputing.

[22]  Kestutis Pyragas Continuous control of chaos by self-controlling feedback , 1992 .

[23]  Xinghuo Yu,et al.  n-scroll chaotic oscillators by second-order systems and double-hysteresis blocks , 2003 .

[24]  Johan A. K. Suykens,et al.  Families of scroll Grid attractors , 2002, Int. J. Bifurc. Chaos.

[25]  Müstak E. Yalçin,et al.  Increasing the Entropy of a Random Number Generator Using n-scroll Chaotic attractors , 2007, Int. J. Bifurc. Chaos.

[26]  Serdar Ozoguz,et al.  n-scroll chaotic attractors from a first-order time-delay differential equation. , 2007, Chaos.

[27]  Bernd Grtner,et al.  Approximation Algorithms and Semidefinite Programming , 2012 .

[28]  Luigi Fortuna,et al.  Implementation and synchronization of 3x3 grid scroll chaotic circuits with analog programmable devices. , 2006, Chaos.

[29]  Toshimitsu Ushio,et al.  Prediction-based control of chaos , 1999 .

[30]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[31]  Ulrich Parlitz,et al.  Stabilizing unstable steady states using multiple delay feedback control. , 2004, Physical review letters.

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

[33]  Simin Yu,et al.  Generation of grid multi-scroll chaotic attractors via switching piecewise linear controller , 2010 .

[34]  Guanrong Chen,et al.  On time-delayed feedback control of chaotic systems , 1999 .

[35]  Noura Mansouri,et al.  Controlling Chaos in Higher-Order Dynamical Systems , 2004, Int. J. Bifurc. Chaos.

[36]  Xinzhi Liu,et al.  Multi-scroll Chaotic and hyperchaotic attractors Generated from Chen System , 2012, Int. J. Bifurc. Chaos.

[37]  Noura Mansouri,et al.  Predictive Control of Continuous Chaotic Systems , 2008, Int. J. Bifurc. Chaos.

[38]  Noura Mansouri,et al.  Control of n-scroll Chua's Circuit , 2009, Int. J. Bifurc. Chaos.

[39]  T. T. Hartley The extended Poincare-Bendixson theorem , 1989 .

[40]  Wenwu Yu,et al.  Synchronization via Pinning Control on General Complex Networks , 2013, SIAM J. Control. Optim..

[41]  Xinghuo Yu,et al.  Fingerprint images encryption via multi-scroll chaotic attractors , 2007, Appl. Math. Comput..

[42]  Xiao-Song Yang,et al.  Generation of multi-scroll delayed chaotic oscillator , 2006 .

[43]  Da Lin,et al.  CONTROLLING THE UNCERTAIN MULTI-SCROLL CRITICAL CHAOTIC SYSTEM WITH INPUT NONLINEAR USING SLIDING MODE CONTROL , 2009 .

[44]  Zhihua Qu Adaptive and robust controls of uncertain systems with nonlinear parameterization , 2003, IEEE Trans. Autom. Control..

[45]  Johan A. K. Suykens,et al.  True random bit generation from a double-scroll attractor , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[46]  J. Sprott Chaotic dynamics on large networks. , 2008, Chaos.

[47]  Guanrong Chen,et al.  Generating Multiscroll Chaotic Attractors: Theories, Methods and Applications , 2006 .