Synchronization of complex-valued neural network with sliding mode control

Abstract In this paper, the synchronization and module-phase synchronization of complex-valued neural network are studied with sliding mode controllers. Both inner synchronization in the same complex-valued neural network and outer synchronization of two complex-valued networks are considered. By separating the real part and imaginary part, a new complex-valued neural network model is provided and module-phase synchronization is defined. With an equivalent linear controller, sliding mode controllers are designed to get the synchronization and module-phase synchronization theorems. Finally, some numerical simulations are presented to show the robustness and effectiveness of our study.

[1]  Chi-Chuan Hwang,et al.  Exponential synchronization of a class of chaotic neural networks , 2005 .

[2]  Shaocheng Tong,et al.  Fuzzy adaptive sliding-mode control for MIMO nonlinear systems , 2003, IEEE Trans. Fuzzy Syst..

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

[4]  Jinde Cao,et al.  Existence and Uniform Stability Analysis of Fractional-Order Complex-Valued Neural Networks With Time Delays , 2015, IEEE Transactions on Neural Networks and Learning Systems.

[5]  B. Rost,et al.  Combining evolutionary information and neural networks to predict protein secondary structure , 1994, Proteins.

[6]  Jürgen Kurths,et al.  Predicting phase synchronization in a spiking chaotic CO2 laser. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  R. P. Marques,et al.  Mixed H2/H∞-control of discrete-time Markovian jump linear systems , 1998, IEEE Trans. Autom. Control..

[8]  Ying Yang,et al.  Predicting dynamic behavior via anticipating synchronization in coupled pendulum-like systems , 2009 .

[9]  Mojtaba Ahmadieh Khanesar,et al.  Adaptive sliding-mode type-2 neuro-fuzzy control of an induction motor , 2015, Expert Syst. Appl..

[10]  Jinde Cao,et al.  Global μ-stability of complex-valued delayed neural networks with leakage delay , 2015, Neurocomputing.

[11]  Takeo Kanade,et al.  Neural Network-Based Face Detection , 1998, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Zidong Wang,et al.  Exponential synchronization of complex networks with Markovian jump and mixed delays , 2008 .

[13]  Jinde Cao,et al.  Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays , 2014, Nonlinear Dynamics.

[14]  Jinde Cao,et al.  Further analysis of global μ-stability of complex-valued neural networks with unbounded time-varying delays , 2015, Neural Networks.

[15]  Mandel,et al.  Single-mode-laser phase dynamics. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[16]  Li-lian Huang,et al.  Dislocation Synchronization of the Different Complex Value Chaotic Systems Based on Single Adaptive Sliding Mode Controller , 2015 .

[17]  Da Lin,et al.  Module-phase synchronization in complex dynamic system , 2010, Appl. Math. Comput..

[18]  Guohui Li.  Modified projective synchronization of chaotic system , 2007 .

[19]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[20]  G. Mahmoud,et al.  Lag synchronization of hyperchaotic complex nonlinear systems , 2012 .

[21]  Jin Bae Park,et al.  Adaptive Neural Sliding Mode Control of Nonholonomic Wheeled Mobile Robots With Model Uncertainty , 2009, IEEE Transactions on Control Systems Technology.

[22]  Zidong Wang,et al.  Robust synchronisation of delayed neural networks with both linear and non-linear couplings , 2009, Int. J. Syst. Sci..

[23]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[24]  Dan Wang,et al.  Neural network-based adaptive dynamic surface control for a class of uncertain nonlinear systems in strict-feedback form , 2005, IEEE Transactions on Neural Networks.

[25]  Emad E. Mahmoud,et al.  Adaptive anti-lag synchronization of two identical or non-identical hyperchaotic complex nonlinear systems with uncertain parameters , 2012, J. Frankl. Inst..

[26]  H. N. Nagaraja,et al.  DSP based proportional integral sliding mode controller for photo-voltaic system , 2015 .

[27]  Gamal M. Mahmoud,et al.  On chaos synchronization of a complex two coupled dynamos system , 2007 .

[28]  F. Varela,et al.  Measuring phase synchrony in brain signals , 1999, Human brain mapping.

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

[30]  Jinde Cao,et al.  Multiple μ-stability analysis of complex-valued neural networks with unbounded time-varying delays , 2015, Neurocomputing.

[31]  H. Haken,et al.  Detuned lasers and the complex Lorenz equations: Subcritical and supercritical Hopf bifurcations. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[32]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.