Global Mittag-Leffler projective synchronization of nonidentical fractional-order neural networks with delay via sliding mode control

Abstract Global Mittag–Leffler projective synchronization for nonidentical delayed fractional-order neural networks based on the technique of delayed sliding mode control is addressed in this paper. Firstly, a delayed fractional-order integral sliding surface is constructed. Then, based on the theory of sliding mode control, a delayed sliding mode controller is designed to ensure the occurrence of sliding motion. Furthermore, based on the fractional Lyapunov direct method and Razumikhin technique, states are converged to the prescribed sliding surface to carry out sliding motion, and some sufficient conditions are derived to realize global Mittag–Leffler projective synchronization of the addressed model. Secondly, as two special cases, complete synchronization and anti-synchronization of the addressed model are investigated. Finally, numerical simulations are presented to illustrate the feasibility and effectiveness of the achieved results.

[1]  Chuandong Li,et al.  Robust Exponential Stability of Uncertain Delayed Neural Networks With Stochastic Perturbation and Impulse Effects , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Xiao Peng,et al.  Global synchronization in finite time for fractional-order neural networks with discontinuous activations and time delays , 2017, Neural Networks.

[3]  S. Das,et al.  Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel , 2010, Appl. Math. Comput..

[4]  Tsung-Chih Lin,et al.  Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems , 2011 .

[5]  Yongguang Yu,et al.  Global attractivity of memristor-based fractional-order neural networks , 2017, Neurocomputing.

[6]  Richard L. Magin,et al.  Fractional calculus models of complex dynamics in biological tissues , 2010, Comput. Math. Appl..

[7]  E. Soczkiewicz,et al.  Application of Fractional Calculus in the Theory of Viscoelasticity , 2002 .

[8]  Lan Xu,et al.  Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems , 2014 .

[9]  Ivanka M. Stamova,et al.  Mittag-Leffler synchronization of fractional neural networks with time-varying delays and reaction-diffusion terms using impulsive and linear controllers , 2017, Neural Networks.

[10]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[11]  I. Stamova.  Global Mittag-Leffler stability and synchronization of impulsive fractional-order neural networks with time-varying delays , 2014, Nonlinear Dynamics.

[12]  Haijun Jiang,et al.  Projective synchronization for fractional neural networks , 2014, Neural Networks.

[13]  Tingwen Huang,et al.  Quantized/Saturated Control for Sampled-Data Systems Under Noisy Sampling Intervals: A Confluent Vandermonde Matrix Approach , 2017, IEEE Transactions on Automatic Control.

[14]  J García-Ojalvo,et al.  Spatiotemporal communication with synchronized optical chaos. , 2000, Physical review letters.

[15]  Weihua Deng,et al.  Remarks on fractional derivatives , 2007, Appl. Math. Comput..

[16]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

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

[18]  Jun Jiang,et al.  Adaptive synchronization of drive-response fractional-order complex dynamical networks with uncertain parameters , 2014, Commun. Nonlinear Sci. Numer. Simul..

[19]  Zhigang Zeng,et al.  Global Mittag-Leffler stability and synchronization of memristor-based fractional-order neural networks , 2014, Neural Networks.

[20]  Wenquan Chen,et al.  Projective synchronization of different fractional-order chaotic systems with non-identical orders , 2012 .

[21]  Haijun Jiang,et al.  Α-stability and Α-synchronization for Fractional-order Neural Networks , 2012, Neural Networks.

[22]  Qing-Long Han,et al.  Global Asymptotic Stability for a Class of Generalized Neural Networks With Interval Time-Varying Delays , 2011, IEEE Trans. Neural Networks.

[23]  Z. Tan,et al.  ASSOCIATIVE MEMORY USING SYNCHRONIZATION IN A CHAOTIC NEURAL NETWORK , 2001 .

[24]  Yaolin Jiang,et al.  Generalized projective synchronization of fractional order chaotic systems , 2008 .

[25]  Ivanka M. Stamova,et al.  Impulsive fractional-order neural networks with time-varying delays: almost periodic solutions , 2017, Neural Computing and Applications.

[26]  Jinde Cao,et al.  Projective synchronization of fractional-order memristor-based neural networks , 2015, Neural Networks.

[27]  M. P. Aghababa.  A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems , 2013 .

[28]  Hongguang Sun,et al.  Fractional diffusion equations by the Kansa method , 2010, Comput. Math. Appl..

[29]  Xing-yuan Wang,et al.  Projective synchronization of fractional order chaotic system based on linear separation , 2008 .

[30]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..

[31]  Yongguang Yu,et al.  Mittag-Leffler stability of fractional-order Hopfield neural networks , 2015 .

[32]  Yu Wang,et al.  Global projective synchronization in finite time of nonidentical fractional-order neural networks based on sliding mode control strategy , 2017, Neurocomputing.

[33]  Zidong Wang,et al.  Guaranteed cost control for uncertain nonlinear systems with mixed time-delays: The discrete-time case , 2018, Eur. J. Control.

[34]  Pietro Cornetti,et al.  Calculation of the tensile and flexural strength of disordered materials using fractional calculus , 2004 .

[35]  Tingwen Huang,et al.  Stabilization for sampled-data systems under noisy sampling interval , 2016, Autom..

[36]  R. Rakkiyappan,et al.  Hybrid projective synchronization of fractional-order memristor-based neural networks with time delays , 2015, Nonlinear Dynamics.

[37]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

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

[39]  Zhixia Ding,et al.  Projective synchronization of nonidentical fractional-order neural networks based on sliding mode controller , 2016, Neural Networks.

[40]  Qiankun Song,et al.  Quasi-uniform synchronization of fractional-order memristor-based neural networks with delay , 2017, Neurocomputing.

[41]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[42]  Ling Liu,et al.  Mittag-Leffler stability of fractional-order neural networks in the presence of generalized piecewise constant arguments , 2017, Neural Networks.

[43]  Changpin Li,et al.  On chaos synchronization of fractional differential equations , 2007 .

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

[45]  Shangbo Zhou,et al.  LAG SYNCHRONIZATION OF THE FRACTIONAL-ORDER SYSTEM VIA NONLINEAR OBSERVER , 2011 .

[46]  Xinghuo Yu,et al.  Sliding Mode Control With Mixed Current and Delayed States for Offshore Steel Jacket Platforms , 2014, IEEE Transactions on Control Systems Technology.

[47]  T. Szabo,et al.  A model for longitudinal and shear wave propagation in viscoelastic media , 2000, The Journal of the Acoustical Society of America.

[48]  Qing-Long Han,et al.  Recent advances in vibration control of offshore platforms , 2017 .