Structure Identification Of Complex Dynamical Networks

Network science has attracted attention of the researchers from various areas in the past 20 years,through establishing corresponding dynamical network models to describe and analyze the physical;biological,social relations,etc.The researchers generally assume that topological structure are known when studying structural properties,dynamical behavior,synchronous control of networks.But in fact,because of the structural complexity of complex dynamical networks and the dynamical complexity of nodes,the topology structure and system parameters may be unknown or uncertain in a lot of cases.Therefore,It is very important to identify topology structure and system parameters.This paper mainly studies the structure identification of complex dynamical networks.Firstly,consider the structure identifica.tion of complex-variable dynamical networks with complex coupling.Using adaptive control scheme to design the corresponding network estimators.According to Barbalat's lemma,two results are derived.Using the Lyapunov function,these results are strictly proved.Two numerical examples illustrate the results effectiveness.Secondly,consider the topology identification of discrete-time delay dynamical networks.Choosing appropriate parameters adaptive update rules to design effective response network esti-mators,to identify the coupling matrix of the uncertain or unknown networks.Using Frobenius matrix norm and Lasalle invariable principle,these methods are proved feasibility.Two numerical examples verify the effectiveness of the proposed method.Thirdly,the structure identification of fractional-order dynamical networks is studied by im-pulsive control.Appropriate impulsive controllers are designed and applied to the dynamical networks with unknown structure.Two results are further proved by using Lyapunov function and illustrated by two numerical examples.Finally,summarize this article.Discuss the recent researches about the structure identification of complex dynamical networks,puts forward some issues worthy of further study.