Research On Synchronization And Control For Several Classes Of Coupled Inertial Neural Networks

Coupled neural network is a special kind of complex networks,and its synchronous behavior has been widely applied in many fields such as information processing,secure communication and objective optimization in recent years.In addition,the second-order inertial neural networks formed by introducing inductance into the circuit can not only simulate many biological characteristics,but also enable the network to have memory disorder search and filtering functions.Moreover,the introduction of inertia term makes the neural network model easier to show complex dynamic behaviors such as bifurcation and chaos,which brings new challenges to the synchronization control of neural networks.In view of the potential biological background and important theoretical value of coupled inertial neural networks,based on the stability theory of differential equations,graph theory,complex network theory,matrix theory,this thesis discusses the exponential synchronization,bipartite synchronization and cluster synchronization of several kinds of coupled inertial delayed neural networks by designing pinning impulsive control,pinning feedback control,event-triggered impulsive control and aperiodically intermittent control,respectively.The exponential synchronization of directed coupled inertial delayed neural networks is investigated based on pinning impulsive control protocol in the third part.Firstly,the original coupled inertial network is equivalently transformed into a first-order differential system by variable substitution.Secondly,based on the reduced-order system,two pinning impulsive control schemes are designed.Finally,the exponential synchronization criteria are established under the strong connectivity by means of the extended Halanay differential inequality,matrix decomposition theory and the concept of average impulsive interval.Actually,the existence of cooperation and competition among nodes in the network may be more in line with practical applications,the bipartite synchronization issue of coupled inertial cooperative-competitive neural networks is investigated by non-reduced order method in the forth part.Firstly,the coopetition interaction networks are characterized by a signed graph.Secondly,for the coupled network with two special structures,i.e.,strong connectivity,containing a directed spanning tree,some pinning feedback control strategies are designed under the assumption that signed digraph is structurally balanced.Finally,by constructing a Lyapunov-Krasovskii functional consisting of state variables and their derivatives,sufficient conditions are established to achieve bipartite synchronization by matrix theory,algebraic graph theory,Barbalat lemma and linear matrix inequality.The event-triggered impulsive control has become a research hotspot in the control field because of its more flexible control mechanism and higher resource utilization.By designing a hybrid event-triggered impulsive control,bipartite synchronization of coupled inertial cooperative-competitive neural networks is studied via non-reduced order method in fifth part.Based on the assumption that the network is structurally balanced and the activation function is bounded,bipartite synchronization criteria in view of algebraic inequalities are established by means of algebraic graph theory,M-matrix theory,Lyapunov method,the concepts of average impulsive interval and average impulsive gain.In view of the potential advantages of the aperiodically intermittent control in information measurement and transmission costs,adaptive aperiodically intermittent control is utilized to explore the pinning exponential synchronization of coupled inertial delayed neural networks in the sixth part.With the help of Lyapunov stability theory,M-matrix theory,linear matrix inequality,the traditional method of constructing a piecewise Lyapunov function is replaced by mathematical analysis technique,the criterion for realizing exponential synchronization is deduced based on the assumption that the network is strongly connected or the network contains a directed spanning tree.It should be pointed out that diffusion effects need to be considered in neural networks and electric circuits when electrons are moving in a nonuniform electromagnetic field,the existing inertial delayed neural network models are improved,and a class of coupled inertial reaction-diffusion delayed neural network models with heterogeneous nodes is proposed in the seventh part.The cluster synchronization is studied by means of pinning control and non-reduced order method.Moreover,two synchronization criteria in terms of the algebraic inequalities are derived under two different communication topologies by utilizing the Lyapunov functional theory,divergence theorem,Barbalat lemma and some basic inequalities.In addition,the above mentioned theoretical results are demonstrated by several numerical examples.