Research On Synchronization Of Three Types Of Complex Networks Based On Optimal Control

From communication networks to transportation networks,power networks,social networks and ecological networks,complex networks are everywhere,and humans have entered the network age.A complex network is composed of a large number of nodes and connecting edges between nodes.It is a highly complex model describing the interrelationships in nature,society,and engineering.Its complexity is reflected in the complexity of nodes and structures,the interaction between structures and nodes,and the interaction between networks.Network synchronization,as an important network coordinated behavior,is one of the key contents of network science research.In recent years,it has become a hot research topic in nonlinear science,and a large number of excellent results have emerged.These results are based on a variety of synchronization modes,and various control strategies are proposed to achieve synchronization control of different network structures.Based on the analysis and summary of current research on network synchronization,this dissertation applies matrix theory,stability theory,control theory,and other optimization control strategies based on aperiodic intermittent control,pinning control,and event-triggered pinning control to several different types of topologies.The network synchronization problem is discussed in depth,and its main work is as follows:First,cluster synchronization of a class of complex networks with non-identical dynamic nodes and coupled time-varying delays is studied by using aperiodically intermittent.The network model discussed not only considers that nodes in different clusters have different dynamic behaviors,but also includes time-varying delays in information transfer between nodes.By applying aperiodic intermittent control strategy and using time-dependent Lyapunov function,combined with matrix inequality,differential inequality and so on,the conditions for ensuring cluster synchronization in this network are theoretically given.These conditions are also suitable for the network synchronization of corresponding identical dynamic nodes,which generalizes the relevant results in the existing research.Considering the uncertainty of network topology changes,this paper also analyzes a class of synchronous control problems for Markov switched networks with incomplete transition rates.The topology of this type of network obeys Markov switching and the transition rate between each mode is unknown or only its estimated value is known,which will be more consistent with the actual network.By constructing the time-dependent Lyapunov-Krasovskii functional,based on a single pinning control method,under the guidance of the stochastic differential dynamic system theory,combined with linear matrix inequalities and extended Jensen inequalities,the stochastic synchronization of this type of network with a transition rate of several cases has been analyzed in detail.The synchronization criteria represented by matrix inequality,which are closely related to network topology switching parameters,are obtained.Finally,event-triggered pinning control is applied to the study of exponentially bounded synchronization of complex networks with mixed delays and external disturbances.In order to effectively save the communication resources between nodes in the network,an event-triggered conditions that depend on the current value of the synchronization error and its previously transmitted value are designed.A relatively novel Lyapunov-Krasovskii function is constructed,and the criterion for the ultimate bounded synchronization of this type of network index is obtained through rigorous theoretical analysis.The upper bound of the synchronization is closely related to the external disturbance parameter properties and related parameters in the designed event-triggered mechanism.At the same time,the Zeno phenomenon that infinite excitation occurs in a limited time under the given event-triggered mechanism and synchronization criterion is also excluded.