A novel adaptive finite-time controller for synchronizing chaotic gyros with nonlinear inputs

In this paper, the problem of the finite-time synchronization of two uncertain chaotic gyros is discussed. The parameters of both the master and the slave gyros are assumed to be unknown in advance. The effects of model uncertainties and input nonlinearities are also taken into account. An appropriate adaptation law is proposed to tackle the gyros' unknown parameters. Based on the adaptation law and the finite-time control technique, proper control laws are introduced to ensure that the trajectories of the slave gyro converge to the trajectories of the master gyro in a given finite time. Simulation results show the applicability and the efficiency of the proposed finite-time controller.

[1]  Her-Terng Yau,et al.  Chaos synchronization of different chaotic systems subjected to input nonlinearity , 2008, Appl. Math. Comput..

[2]  Henry Leung,et al.  Experimental verification of multidirectional multiscroll chaotic attractors , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  关新平,et al.  Adaptive synchronization with nonlinear input , 2005 .

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

[5]  H.-K. Chen.  CHAOS AND CHAOS SYNCHRONIZATION OF A SYMMETRIC GYRO WITH LINEAR-PLUS-CUBIC DAMPING , 2002 .

[6]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[7]  姜长生,et al.  Chaos synchronization between two different 4D hyperchaotic Chen systems , 2007 .

[8]  吕翎,et al.  Generalized chaos synchronization of a weighted complex network with different nodes , 2010 .

[9]  Teh-Lu Liao,et al.  Generalized projective synchronization of chaotic nonlinear gyros coupled with dead-zone input , 2008 .

[10]  Dennis S. Bernstein,et al.  Finite-Time Stability of Continuous Autonomous Systems , 2000, SIAM J. Control. Optim..

[11]  张卫东,et al.  Chaotic synchronization via linear controller , 2007 .

[12]  Z. Ge,et al.  Bifurcations and chaos in a rate gyro with harmonic excitation , 1996 .

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

[14]  Her-Terng Yau,et al.  Nonlinear rule-based controller for chaos synchronization of two gyros with linear-plus-cubic damping ☆ , 2007 .

[15]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

[16]  Hu Jia,et al.  Adaptive synchronization of uncertain Liu system via nonlinear input , 2008 .

[17]  Guanrong Chen,et al.  Theoretical Design and Circuit Implementation of Multidirectional Multi-Torus Chaotic Attractors , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[18]  Lee Sun-Jin.  From Chaos to Order , 2011 .

[19]  Bo Wang,et al.  On the synchronization of a class of chaotic systems based on backstepping method , 2007 .

[20]  Jinde Cao,et al.  Local Synchronization of a Complex Network Model , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[21]  C. K. Michael Tse,et al.  Adaptive Feedback Synchronization of a General Complex Dynamical Network With Delayed Nodes , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[22]  Di Zhou,et al.  Adaptive Nonlinear Synchronization Control of Twin-Gyro Precession , 2006 .

[23]  Jun-Juh Yan,et al.  Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters , 2006 .

[24]  X. Tong,et al.  Chaotic Motion of a Symmetric Gyro Subjected to a Harmonic Base Excitation , 2001 .

[25]  Wei Xu,et al.  Synchronization of two chaotic nonlinear gyros using active control , 2005 .

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

[27]  Henry Leung,et al.  Design and implementation of n-scroll chaotic attractors from a general jerk circuit , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[28]  H.-K. Chen,et al.  Synchronization of chaotic symmetric gyros by one-way coupling conditions , 2003 .

[29]  Her-Terng Yau,et al.  Chaos synchronization of two uncertain chaotic nonlinear gyros using fuzzy sliding mode control , 2008 .

[30]  Xinghuo Yu,et al.  Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method , 2004, Autom..

[31]  Li Guo-Hui,et al.  Chaos synchronization based on intermittent state observer , 2004 .

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

[33]  R. V. Dooren,et al.  Comments on “Chaos and chaos synchronization of a symmetric gyro with linear-plus-cubic damping” , 2003 .

[34]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[35]  H. Salarieh,et al.  Chaos synchronization of nonlinear gyros in presence of stochastic excitation via sliding mode control , 2008 .

[36]  M. P. Aghababa,et al.  Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique , 2011 .

[37]  Xinghuo Yu,et al.  Design and analysis of multiscroll chaotic attractors from saturated function series , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[38]  Junan Lu,et al.  Pinning adaptive synchronization of a general complex dynamical network , 2008, Autom..