Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

In this paper, a class of fractional complex networks with impulses and reaction–diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results.

[1]  Xinchu Fu,et al.  Cluster synchronization in community networks with nonidentical nodes. , 2009, Chaos.

[2]  Wei-Ying Ding,et al.  A Closed-Form Solution for the Impedance Calculation of Grid Power Distribution Network , 2017, IEEE Transactions on Electromagnetic Compatibility.

[3]  Yi Zhao,et al.  Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control , 2016, Appl. Math. Comput..

[4]  Jinde Cao,et al.  Stability Analysis of Markovian Jump Stochastic BAM Neural Networks With Impulse Control and Mixed Time Delays , 2012, IEEE Transactions on Neural Networks and Learning Systems.

[5]  Jing Huang,et al.  State Estimation in Electric Power Grids: Meeting New Challenges Presented by the Requirements of the Future Grid , 2012, IEEE Signal Processing Magazine.

[6]  Oh-Min Kwon,et al.  Closeness-Centrality-Based Synchronization Criteria for Complex Dynamical Networks With Interval Time-Varying Coupling Delays , 2018, IEEE Transactions on Cybernetics.

[7]  Clara-Mihaela Ionescu,et al.  The role of fractional calculus in modeling biological phenomena: A review , 2017, Commun. Nonlinear Sci. Numer. Simul..

[8]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[9]  Yongguang Yu,et al.  Mean-square consensus of heterogeneous multi-agent systems with nonconvex constraints, Markovian switching topologies and delays , 2018, Neurocomputing.

[10]  Huai-Ning Wu,et al.  Passivity of delayed reaction-diffusion networks with application to a food web model , 2013, Appl. Math. Comput..

[11]  Wei Jiang,et al.  Synchronization analysis of singular dynamical networks with unbounded time-delays , 2015, Advances in Difference Equations.

[12]  Rathinasamy Sakthivel,et al.  Disturbance and uncertainty rejection performance for fractional-order complex dynamical networks , 2019, Neural Networks.

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

[14]  Junguo Lu.  Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions , 2008 .

[15]  Wenwu Yu,et al.  Synchronization on Complex Networks of Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[16]  Zidong Wang,et al.  Event-based state estimation for a class of complex networks with time-varying delays: A comparison principle approach , 2017 .

[17]  Wenwu Yu,et al.  Synchronizing nonlinear complex networks via switching disconnected topology , 2016, Autom..

[18]  Richard L. Magin,et al.  On the fractional signals and systems , 2011, Signal Process..

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

[20]  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.

[21]  Feiqi Deng,et al.  Pointwise-in-space stabilization and synchronization of a class of reaction–diffusion systems with mixed time delays via aperiodically impulsive control , 2017 .

[22]  Jing-Wen Yi,et al.  Adaptive pinning cluster synchronization of fractional-order complex dynamical networks , 2014, Appl. Math. Comput..

[23]  Wu Jigang,et al.  Pinning Control for Synchronization of Coupled Reaction-Diffusion Neural Networks With Directed Topologies , 2016, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[24]  Peng Lin,et al.  Distributed consensus of second‐order multiagent systems with nonconvex input constraints , 2018 .

[25]  Junzhi Yu,et al.  Global stability analysis of fractional-order Hopfield neural networks with time delay , 2015, Neurocomputing.

[26]  Hongtao Lu,et al.  Projective lag synchronization of the general complex dynamical networks with distinct nodes , 2012 .

[27]  Lada A. Adamic,et al.  Internet: Growth dynamics of the World-Wide Web , 1999, Nature.

[28]  Fangfang Zhang,et al.  Complex function projective synchronization of complex chaotic system and its applications in secure communication , 2013, Nonlinear Dynamics.

[29]  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 .

[30]  Oh-Min Kwon,et al.  Synchronization of fractional-order complex dynamical network with random coupling delay, actuator faults and saturation , 2018 .

[31]  M. Abbaszadeh,et al.  Nonlinear observer design for one-sided Lipschitz systems , 2010, Proceedings of the 2010 American Control Conference.

[32]  Huijun Gao,et al.  Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control , 2014, Autom..

[33]  Wei Xing Zheng,et al.  Generalized synchronization of complex dynamical networks via impulsive control. , 2009, Chaos.

[34]  Zhenjiang Zhao,et al.  Global exponential stability of complex-valued neural networks with both time-varying delays and impulsive effects , 2016, Neural Networks.

[35]  Margarita Rivero,et al.  Stability of Fractional Order Systems , 2013 .

[36]  Tianping Chen,et al.  Synchronization of Complex Networks via Aperiodically Intermittent Pinning Control , 2015, IEEE Transactions on Automatic Control.

[37]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[38]  Xiaoli Zhang,et al.  Effect of delayed impulses on input-to-state stability of nonlinear systems , 2017, Autom..

[39]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[40]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[41]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[42]  Jing-Wen Yi,et al.  Exponential synchronization of complex dynamical networks with markovian jump parameters and stochastic delays and its application to multi-agent systems , 2013, Commun. Nonlinear Sci. Numer. Simul..

[43]  Lei Guo,et al.  Novel Adaptive Strategies for Synchronization of Linearly Coupled Neural Networks With Reaction-Diffusion Terms , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[44]  Yi Chai,et al.  Adaptive pinning synchronization in fractional-order complex dynamical networks , 2012 .

[45]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[46]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[47]  Zidong Wang,et al.  Pinning controllability of autonomous Boolean control networks , 2016, Science China Information Sciences.

[48]  Christophe Farges,et al.  A stability test for non-commensurate fractional order systems , 2010, Syst. Control. Lett..