Convergence Control Of Dynamic Network Systems With Communication Constraints

With the development of network science,the research of dynamic network system has been paid more and more attention in the field of science and engineering.In real life,many systems exist in the form of network,but early network research mainly focused on describing problems with simple regular network.With the differential equation gradually known,people find that many practical problems in reality can be described by a dynamic network model.At present,the dynamic analysis of network system has gradually become a research hotspot for scholars.Based on the existing results,this paper discusses the problem of finite-time anti-synchronization and state estimation of neural networks under the influence of time-varying delay.At the same time,based on sampled-data control,for complex networks and multi-agent systems with communication constraints,the lag synchronization problem and the consensus problem are studied,respectively.In addition,the consensus problem of multi-agent system is discussed under switching topology.The theoretical results of this paper have been verified by numerical simulation,and the main research contents are as follows:(1)For neural networks with time delay,the finite-time anti-synchronization problem is studied.By using the finite-time stability theory and some differential inequality methods,the finite-time anti-synchronization criterion are obtained under the intermittent feedback controller.In addition,based on the sampled-data state estimator,the state estimation of competitive neural network with communication constraints is studied.By introducing a switching signal,a switching system is obtained to describe whether the network has packet loss.Then,the upper bound of packet loss rate is calculated.Using the average dwell time theory,the state of the competitive neural network can be estimated when the packet loss rate is less than or equal to its upper bound for any switching signal.(2)The lag synchronization problem of complex networks with communication constraints is studied.Introducing a Bernoulli random variable,the information of probabilistic time-varying delay is converted into a deterministic time-varying delay with random parameters.Similarly,since packet loss may occur in the system,the error system is converted to a switching system to describe the packet loss of the system.Then,a stochastic sampling controller with m sampling intervals is designed,and sufficient conditions for lag synchronization of complex networks are obtained by using Lyapunov stability theory and basic inequality method.(3)For a nonlinear multi-agent system with communication constraints,the problem of sample-data consensus is studied.On the one hand,By introducing a Bernoulli distribution sequence is used to describe the random packet loss.On the other hand,define a switching signal,a switched system can be obtained to describe the packet loss of the system in a certain way.Based on the special properties of Laplace matrix,the consensus problem can be transformed into the stability problem of error systems with lower dimensions.By giving different maximum sampling intervals,different convergence speeds of the system are obtained.Finally,a sampled data control protocol is designed,and the consensus criterion of multi-agent system is derived.(4)For the multi-agent system with randomly occurring nonlinearities and the nonlinear multi-agent system with randomly varying nonlinearities,the consensus problem under switching topology is studied.Firstly,by defining the error system,the consensus of the system can be transformed into the stability of the error system.Then,when all the topologies contain a directed spanning tree,by designing an appropriate control protocol,since the topological structure is switched,the uncertain pinning nodes are selected,and the consensus criterion of multi-agent system is established.Secondly,considering that the follower can not receive information of the leader in part of the topology graph,that is,when the topology graph does not contain a directed spanning tree,the consensus criteria of the system can still be obtained.