Modified function projective synchronization between two fractional-order complex dynamical networks with unknown parameters and unknown bounded external disturbances

Abstract This paper investigates the problem of modified function projective synchronization between two fractional-order complex dynamical networks with unknown parameters and unknown bounded external disturbances. Based on the stability theory of fractional-order differential system, a new robust adaptive control scheme is designed to achieve modified function projective synchronization for two fractional-order complex dynamical networks, which is able to estimate all unknown parameters and attenuate all random uncertainties of the fractional-order complex dynamical networks. Moreover, there is no need to know the norm-bounds of all random uncertainties, and the compensator gains can be automatically adapted to suitable constants. Numerical examples are provided to show the effectiveness of proposed methods.

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

[2]  Yong Chen,et al.  FUNCTION PROJECTIVE SYNCHRONIZATION BETWEEN TWO IDENTICAL CHAOTIC SYSTEMS , 2007 .

[3]  Manuel A. Duarte-Mermoud,et al.  Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[4]  Grzegorz Litak,et al.  Finite-time synchronization of fractional-order simplest two-component chaotic oscillators , 2017, The European Physical Journal B.

[5]  W. K. Wong,et al.  Robust synchronization of fractional-order complex dynamical networks with parametric uncertainties , 2012 .

[6]  M. Duarte-Mermoud,et al.  Boundedness of the solutions for certain classes of fractional differential equations with application to adaptive systems. , 2016, ISA transactions.

[7]  Hongyue Du,et al.  Modified function projective synchronization of chaotic system , 2009 .

[8]  Zhenyuan Xu,et al.  Function projective synchronization in drive–response dynamical network , 2010 .

[9]  Yu Wang,et al.  Synchronization of fractional order complex dynamical networks , 2015 .

[10]  Tene Alain Giresse,et al.  Chaos generalized synchronization of coupled Mathieu-Van der Pol and coupled Duffing-Van der Pol systems using fractional order-derivative , 2017 .

[11]  Wei Zhu,et al.  Function projective synchronization for fractional-order chaotic systems , 2011 .

[12]  Manuel A. Duarte-Mermoud,et al.  On the Lyapunov theory for fractional order systems , 2016, Appl. Math. Comput..

[13]  R. Tchitnga,et al.  Generalized finite-time function projective synchronization of two fractional-order chaotic systems via a modified fractional nonsingular sliding mode surface , 2017 .

[14]  Hongyue Du.  Adaptive Open-Plus-Closed-Loop Control Method Of Modified Function Projective Synchronization In Complex Networks , 2011 .

[15]  R. Tchitnga,et al.  Dynamical Properties and Finite-Time Hybrid Projective Synchronization Using Fractional Nonsingular Sliding Mode Surface in Fractional-Order Two-Stage Colpitts Oscillators , 2013 .

[16]  Ranchao Wu,et al.  Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay , 2016 .

[17]  Gamal M. Mahmoud,et al.  Active control technique of fractional-order chaotic complex systems , 2016 .

[18]  Jinde Cao,et al.  Finite-time synchronization of fractional-order memristor-based neural networks with time delays , 2016, Neural Networks.

[19]  Hongyue Du,et al.  Function projective synchronization in drive–response dynamical networks with non-identical nodes☆ , 2011 .

[20]  Yu Wang,et al.  Outer synchronization of fractional-order complex dynamical networks , 2016 .

[21]  Peng Shi,et al.  Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control , 2013 .

[22]  Gamal M. Mahmoud,et al.  On fractional-order hyperchaotic complex systems and their generalized function projective combination synchronization , 2017 .

[23]  Anaclet Fomethe,et al.  On the relay coupling of three fractional-order oscillators with time-delay consideration: Global and cluster synchronizations , 2018, Chaos, Solitons & Fractals.

[24]  Emad E. Mahmoud,et al.  Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control , 2017 .

[25]  Chunguang Li,et al.  Chaos in the fractional order Chen system and its control , 2004 .

[26]  Gamal M. Mahmoud,et al.  Generalization of combination–combination synchronization of chaotic n-dimensional fractional-order dynamical systems , 2016 .

[27]  Chengren Li,et al.  Outer synchronization between uncertain networks with adaptive scaling function and different node numbers , 2018 .

[28]  Jinde Cao,et al.  Dissipativity and stability analysis of fractional-order complex-valued neural networks with time delay , 2017, Neural Networks.

[29]  Jinde Cao,et al.  Synchronization of fractional-order complex-valued neural networks with time delay , 2016, Neural Networks.

[30]  Hongyue Du,et al.  Function projective synchronization in coupled chaotic systems , 2010 .

[31]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[32]  Xiang Li,et al.  Phase synchronization in complex networks with decayed long-range interactions , 2006 .

[33]  Jigen Peng,et al.  Synchronization of fractional-order linear complex networks with directed coupling topology , 2018 .

[34]  Jinde Cao,et al.  Adaptive synchronization of fractional-order memristor-based neural networks with time delay , 2015, Nonlinear Dynamics.

[35]  Guanrong Chen,et al.  Chaos synchronization of general complex dynamical networks , 2004 .

[36]  Huaguang Zhang,et al.  Observer-based lag synchronization between two different complex networks , 2014, Commun. Nonlinear Sci. Numer. Simul..

[37]  K. Sudheer,et al.  Function projective synchronization in chaotic and hyperchaotic systems through open-plus-closed-loop coupling. , 2010, Chaos.

[38]  Hongtao Lu,et al.  Hyperchaotic secure communication via generalized function projective synchronization , 2011 .

[39]  Xingyuan Wang,et al.  Projective synchronization of a complex network with different fractional order chaos nodes , 2011 .

[40]  Elena Grigorenko,et al.  Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.