Single input sliding mode control for hyperchaotic Lu system with parameter uncertainty

In this paper, design of sliding mode controller (SMC) is presented to investigate the stabilization, complete synchronization and adaptive synchronization of four dimensional hyperchaotic Lu systems with parameter uncertainty. To achieve this goal, sliding mode control scheme along with Lyapunov stability theory is utilized. A proportional integral switching surface is proposed to ensure the stability of the closed-loop system in sliding motion. The SMC has been proposed to guarantee the occurrence of the sliding motion. It has also been shown that by proper choice of the adaptation laws for parameters, systems can be synchronized in conventional manner in master-slave configuration, in uncertain environment. The proposed adaptation laws also ensure the convergence of uncertain parameters to their true value in all the cases. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed approach.

[1]  Xiaohua Xiong,et al.  Conjugate Lorenz-type chaotic attractors , 2009 .

[2]  Daolin Xu,et al.  Controlling the ultimate state of projective synchronization in chaotic systems of arbitrary dimension. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Xuefei Liu,et al.  Feedback and adaptive control and synchronization of a set of chaotic and hyperchaotic systems , 2007 .

[4]  Indra Narayan Kar,et al.  Contraction theory based adaptive synchronization of chaotic systems , 2009 .

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

[6]  Guanrong Chen,et al.  Synchronization Transition Induced by Synaptic Delay in Coupled Fast-Spiking Neurons , 2008, Int. J. Bifurc. Chaos.

[7]  M. M. El-Dessoky,et al.  Adaptive synchronization of a hyperchaotic system with uncertain parameter , 2006 .

[8]  Chi-Ching Yang,et al.  Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller , 2011 .

[9]  Xiaofeng Liao,et al.  Impulsive control, complete and lag synchronization of unified chaotic system with continuous periodic switch , 2005 .

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

[11]  A. E. Matouk,et al.  Chaos Synchronization between Two Different Fractional Systems of Lorenz Family , 2009 .

[12]  Weiping Li,et al.  Applied Nonlinear Control , 1991 .

[13]  Satnesh Singh,et al.  Sliding Mode Control Based Anti-Synchronization Scheme for Hyperchaotic Lu Systems , 2011, 2011 International Conference on Communication Systems and Network Technologies.

[14]  Uchechukwu E. Vincent,et al.  Phase synchronization in bi-directionally coupled chaotic ratchets , 2006 .

[15]  Daolin Xu,et al.  A secure communication scheme using projective chaos synchronization , 2004 .

[16]  Zheng-Ming Ge,et al.  Generalized synchronization of chaotic systems by pure error dynamics and elaborate Lyapunov function , 2009 .

[17]  X. Liao,et al.  Fuzzy modeling and synchronization of hyperchaotic systems , 2005 .

[18]  Zhaosheng Feng,et al.  Synchronization transition in gap-junction-coupled leech neurons , 2008 .

[19]  Wei Xu,et al.  Adaptive generalized projective synchronization in different chaotic systems based on parameter identification , 2007 .

[20]  Indra Narayan Kar,et al.  Observer-based synchronization scheme for a class of chaotic systems using contraction theory , 2011 .

[21]  Santo Banerjee,et al.  FUNCTIONAL SYNCHRONIZATION AND ITS APPLICATION TO SECURE COMMUNICATIONS , 2009 .

[22]  Wuneng Zhou,et al.  On dynamics analysis of a new chaotic attractor , 2008 .

[23]  Yonglu Shu,et al.  Switching among three different kinds of synchronization for delay chaotic systems , 2005 .

[24]  W. Zhang,et al.  LMI criteria for robust chaos synchronization of a class of chaotic systems , 2007 .

[25]  M. Noorani,et al.  Adaptive reduced-order anti-synchronization of chaotic systems with fully unknown parameters , 2010 .

[26]  Xuebing Zhang,et al.  Anti-synchronization of Two Different Hyperchaotic Systems via Active and Adaptive Control , 2008 .

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

[28]  I. Kar,et al.  Parametric convergence and control of chaotic system using adaptive feedback linearization , 2009 .

[29]  Qing Wang,et al.  Robust Synchronization of Hyperchaotic Systems with Uncertainties and External Disturbances , 2014, J. Appl. Math..

[30]  Satnesh Singh,et al.  Active control systems for anti-synchronization based on sliding mode control , 2011, 2011 2nd International Conference on Computer and Communication Technology (ICCCT-2011).

[31]  Satnesh Singh,et al.  Sliding mode control-based stabilisation and secure communication scheme for hyperchaotic systems , 2012, Int. J. Autom. Control..

[32]  Huijun Gao,et al.  Distributed Synchronization in Networks of Agent Systems With Nonlinearities and Random Switchings , 2013, IEEE Transactions on Cybernetics.

[33]  Chi-Ching Yang,et al.  Adaptive Single Input Control for Synchronization of a 4D Lorenz–Stenflo Chaotic System , 2014 .

[34]  Guanrong Chen,et al.  Bifurcation Analysis of Chen's equation , 2000, Int. J. Bifurc. Chaos.