| Many actual network systems can be represented by complex network models,and complex networks exhibit various dynamic behaviors related to our production and life.Synchronization,as an important dynamic behavior of complex networks,has attracted the attention of many scholars.A lot of research results have been achieved.However,under time delays and disturbances,the synchronization and control of single-layer and its multilayer dissipative networks are worthy of further study.Based on the research of previous researchers,this paper uses stability theory,feedback and adaptive control technology to study the synchronization and control problems between single-layer and multi-layer networks.Main tasks are as follows:1.The synchronization problem of complex networks with random uncertainty and time delay is studied.Based on the Lyapunov-Krasovskii functional theory,some sufficient conditions about the inner synchronization of networks are obtained.In view of the random uncertainty in the network,nonlinear adaptive controllers are designed,and adaptive update laws are used to process the feedback factors.The designed nonlinear adaptive controller can be used not only for network synchronization with time-delay nodes,but also for network synchronization with time-delay random noise and time-delay nodes.2.Discuss the fixed-time external synchronization problem between two-layer networks with different topologies under random disturbance.In order to ensure that the two-layer dynamic network achieves fixed-time point-to-point synchronization under random disturbances,and to suppress chattering during the synchronization process between two-layer networks of different topologies,a continuous feedback controller without chattering is designed.Using Lyapunov stability theory,the conditions for synchronization between networks are obtained.3.The problem of fixed-time external synchronization between two-layer time-delay neuron networks composed of nonlinear dynamic systems with uncertain parameters is studied.To solve this problem,we propose a time-delay dependent controller.Using Lyapunov stability theory,sufficient conditions for fixed-time external synchronization between two-layer time-delay neural networks are given.In order to ensure the identification of uncertain parameters,an adaptive update identification law is designed.The designed controller,adaptive update identification law and sufficient conditions are not only suitable for fixed-time external synchronization between undirected networks,but also for fixed-time external synchronization between directed networks.The research results show that in synchronization,the fixed setting time is related to the design of the controller,the size of the network,the number of uncertain parameters of each neuron and the dimension of each neuron node.4.The problem of fixed time out-of-time synchronization between multiple hybrid link networks is studied.In order to achieve synchronization between multiple hybrid link networks with neuron nodes and time-varying delays,a state-delay-dependent feedback fixed-time controller is designed.In order to ensure fixed time synchronization between multiple hybrid link networks with or without time delay,some sufficient conditions for synchronization are given.The designed state-delay-dependent feedback controller and sufficient conditions are not only suitable for fixed time synchronization between multiple hybrid link undirected networks,but also for fixed time synchronization of multiple hybrid link directed networks.The fixed setup time is related to the designed controller parameters,the number of nodes in the multi-hybrid link network and the dimension of the node status in the network.5.The problem of fixed-time external synchronization between double-layer multiple coupled networks with random disturbances is studied.In order to suppress chattering during synchronization,an adaptive non-chattering control algorithm is designed.Based on the Lyapunov stability theory,sufficient conditions for adaptive random external synchronization are given.The designed adaptive chatter-free controller and sufficient conditions for synchronization are not only suitable for the fixed-time synchronization of multiple coupled undirected networks under random disturbances,but also for the fixedtime random synchronization of multiple coupled directed networks under random disturbances.Our theoretical results show that in fixed-time random external synchronization,the fixed setting time is related to the scale of the dynamic network,the dimension of the node,and the designed adaptive controller. |
