Adaptive synchronization for two identical generalized Lorenz chaotic systems via a single controller

Abstract This paper presents a systematic design procedure to synchronize two identical generalized Lorenz chaotic systems based on a sliding mode control. In contrast to the previous works, this approach only needs a single controller to realize synchronization, which has considerable significance in reducing the cost and complexity for controller implementation. A switching surface only including partial states is adopted to ensure the stability of the error dynamics in the sliding mode. Then an adaptive sliding mode controller (ASMC) is derived to guarantee the occurrence of the sliding motion even when the parameters of the drive and response generalized Lorenz systems are unknown. Last, an example is included to illustrate the results developed in this paper.

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

[2]  Her-Terng Yau,et al.  Synchronization and anti-synchronization coexist in two-degree-of-freedom dissipative gyroscope with nonlinear inputs , 2008 .

[3]  Yeong-Jeu Sun,et al.  Solution bounds of generalized Lorenz chaotic systems , 2009 .

[4]  Denis Efimov.  Dynamical adaptive synchronization , 2006 .

[5]  Donghua Zhou,et al.  A new observer-based synchronization scheme for private communication , 2005 .

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

[7]  Vadim I. Utkin,et al.  Sliding Modes and their Application in Variable Structure Systems , 1978 .

[8]  Xinghuo Yu,et al.  Chaos Synchronization via Controlling Partial State of Chaotic Systems , 2001, Int. J. Bifurc. Chaos.

[9]  Tzuyin Wu,et al.  Chaos control of the modified Chua's circuit system , 2002 .

[10]  Vasile Mihai Popov,et al.  Hyperstability of Control Systems , 1973 .

[11]  T. Liao,et al.  Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity , 2008 .

[12]  Xinghuo Yu,et al.  Stabilizing unstable periodic orbits of chaotic systems via an optimal principle , 2000, J. Frankl. Inst..

[13]  Pei Yu,et al.  Chaos control and synchronization for a special generalized Lorenz canonical system – The SM system , 2009 .

[14]  Aria Alasty,et al.  Chaotic motions and fractal basin boundaries in spring-pendulum system , 2006 .

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

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

[17]  Sarah K. Spurgeon,et al.  Sliding mode observers for fault detection and isolation , 2000, Autom..

[18]  Roland Schmitz,et al.  Use of chaotic dynamical systems in cryptography , 2001, J. Frankl. Inst..

[19]  J. Yan,et al.  Robust synchronization of chaotic systems via adaptive sliding mode control , 2006 .

[20]  Shihua Chen,et al.  Impulsive control and synchronization of unified chaotic system , 2004 .

[21]  H. Yau,et al.  Chaos synchronization using fuzzy logic controller , 2008 .

[22]  Ouaténi Diallo,et al.  Melnikov analysis of chaos in a general epidemiological model , 2007 .

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

[24]  Qidi Wu,et al.  Impulsive control for the stabilization and synchronization of Lorenz systems , 2002 .

[25]  Guanrong Chen,et al.  Effective chaotic orbit tracker: a prediction-based digital redesign approach , 2000 .

[26]  Antônio de Pádua Braga,et al.  Sliding mode neural network control of an induction motor drive , 2003 .