A general approach for synchronisation of nonlinear networked systems with switching topology

This article investigates synchronisation of a nonlinear networked system with switching topology. By defining a common synchronisation manifold for each possible switching topology, exponential synchronisation of a nonlinear networked system can be assessed by the exponential stability of a reduced nonlinear system corresponding to the concerned system, wherein the communication graph can be directed and weighted and the inner-linking matrix might be singular. In particular, a synchronisation criterion consisting of the self-dynamics of isolated nodes and the consensus dynamics of a linear switched system is given. Two numerical simulations of synchronisation are presented to illustrate the effectiveness of the analytical results for the periodic and random switching cases.

[1]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[2]  Tianping Chen,et al.  Synchronization in general complex delayed dynamical networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

[3]  W. Arthur,et al.  The Economy as an Evolving Complex System II , 1988 .

[4]  M Chavez,et al.  Synchronization in dynamical networks: evolution along commutative graphs. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Erik M. Bollt,et al.  Sufficient Conditions for Fast Switching Synchronization in Time-Varying Network Topologies , 2006, SIAM J. Appl. Dyn. Syst..

[6]  Daizhan Cheng,et al.  Synchronisation of a class of networked passive systems with switching topology , 2009, Int. J. Control.

[7]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[8]  Chai Wah Wu,et al.  Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Guanrong Chen,et al.  Global synchronization and asymptotic stability of complex dynamical networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  F. Zou,et al.  Bifurcation and chaos in cellular neural networks , 1993 .

[11]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[12]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[13]  Mario di Bernardo,et al.  Contraction Theory and Master Stability Function: Linking Two Approaches to Study Synchronization of Complex Networks , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[14]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2009, Autom..

[15]  Guangming Xie,et al.  Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays , 2008, Syst. Control. Lett..

[16]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[17]  Ji Xiang,et al.  On local synchronisability of nonlinear networked systems with a unit inner-coupling matrix and switching topology , 2011, Int. J. Control.

[18]  Xiaoming Hu,et al.  Synchronization of a class of networked passive systems with switching topology , 2007, 2007 46th IEEE Conference on Decision and Control.

[19]  Lan V. Zhang,et al.  Evidence for dynamically organized modularity in the yeast protein–protein interaction network , 2004, Nature.

[20]  Lan Xiang,et al.  Impulsive consensus seeking in directed networks of multi-agent systems with communication time delays , 2012, Int. J. Syst. Sci..

[21]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[22]  M. Hasler,et al.  Blinking model and synchronization in small-world networks with a time-varying coupling , 2004 .

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

[24]  A. Jadbabaie,et al.  Synchronization in Oscillator Networks: Switching Topologies and Non-homogeneous Delays , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[25]  Haibo Jiang,et al.  Consensus of multi-agent linear dynamic systems via impulsive control protocols , 2011, Int. J. Syst. Sci..

[26]  Manfredi Maggiore,et al.  Necessary and sufficient graphical conditions for formation control of unicycles , 2005, IEEE Transactions on Automatic Control.

[27]  Maoyin Chen,et al.  Synchronization in time-varying networks: a matrix measure approach. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .

[29]  Jean-Jacques E. Slotine,et al.  Stable concurrent synchronization in dynamic system networks , 2005, Neural Networks.

[30]  Jun Zhao,et al.  Synchronization of Complex Dynamical Networks with Switching Topology: a Switched System Point of View , 2008 .

[31]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2005, IEEE Transactions on Automatic Control.

[32]  Hardy Hanappi,et al.  The Economy as an Evolving Complex System: V.3 by Lawrence E. Blume and Steven N. Durlauf , 2007, Journal of Artificial Societies and Social Simulation.

[33]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[34]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[35]  Z. Duan,et al.  Network synchronizability analysis: a graph-theoretic approach. , 2008, Chaos.

[36]  E. Marder,et al.  Plasticity in single neuron and circuit computations , 2004, Nature.

[37]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[38]  Alain Destexhe,et al.  Neuronal Computations with Stochastic Network States , 2006, Science.

[39]  Daniel W. C. Ho,et al.  Globally Exponential Synchronization and Synchronizability for General Dynamical Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[40]  Wei Xing Zheng,et al.  On average consensus in directed networks of agents with switching topology and time delay , 2011, Int. J. Syst. Sci..

[41]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[42]  Daizhan Cheng,et al.  Lyapunov-Based Approach to Multiagent Systems With Switching Jointly Connected Interconnection , 2007, IEEE Transactions on Automatic Control.

[43]  Lei Wang,et al.  Synchronization in complex networks with switching topology , 2011 .

[44]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[45]  Rodolphe Sepulchre,et al.  Synchronization in networks of identical linear systems , 2008, 2008 47th IEEE Conference on Decision and Control.