Event-based Synchronization Of Networks With Variable Gain

Many large-scale systems composed of independent units,such as neural networks,multi-UAV systems,coupled circuits,etc.,may achieve the same dynamics through the interaction between the units.This phenomenon is called synchronization,which has important application value in many fields,and the research on synchronization phenomenon can also be expressed as the synchronization problem of complex dynamic network.In practice,due to the influence of various factors,the interaction between these independent units is not fixed,and the corresponding coupling gain often changes with time.Therefore,how to reach the synchronization of complex networks with variable gain is very important.At the same time,the time required to achieve network synchronization is also a problem that cannot be ignored.Nowadays,many researches aim to realize the asymptotic synchronization or exponential synchronization of the network,and the required synchronization time tends to be infinite,which cannot meet the needs of practical engineering.In addition,the number of control is also a factor that has to be considered in practical engineering.At present,event-triggered control is gradually becoming an effective method to save control resources.In this paper,for a class of complex dynamic networks with variable gain,by designing effective event-triggered control schemes,the exponential synchronization and prescribed time synchronization of networks with nonlinear nodes are studied respectively.On the one hand,for a class of dynamic networks composed of nonlinear systems with self-delay,it is assumed that the network topology is a directed network,including a leader and multiple followers,and there is intermittent coupling between network nodes.This paper proposes to express the intermittent coupling as a control protocol with variable gain,and introduces an event-triggered mechanism.The update of the control signal relies on a simple exponential function,which effectively reduces the redundant execution times of the control.Under this control scheme,we establish synchronization conditions based on the average gain over a single intermittent period and give an estimate of the maximum allowable delay.It is worth pointing out that the obtained synchronization conditions are also applicable to the continuously changing coupling gain,such as the case where the gain function is a piecewise linear function or a nonlinear function.Numerical simulations also demonstrate the validity of the control protocol and the correctness of the obtained synchronization conditions.On the other hand,by designing a class of variable-gain control protocols,this paper also studies the prescribed time synchronization problem of dynamic networks with nodes with Lipschitz nonlinearity.We first establish a new lemma on predetermined time stability,and then design an event-triggered control scheme based on time-varying gain.In order to save the computational cost,we adopt a simple time-based trigger condition,and the control signals of each node are updated discretely.It can be proved that the network can be synchronized within a predetermined length of time,and the Zeno phenomenon will not appear during the control process;at the same time,the control signal always remains bounded when the control gain changes.Finally,the validity of the theoretical results is verified by numerical simulation.Compared with the existing researches,the main difference of this paper is that the variable-gain coupling control and the event-triggered control are combined,and two situations are studied respectively in the dynamic network where the node time is delayed and the synchronization time can be preset,and the Give simple synchronization sufficient conditions.The research in this paper provides theoretical guidance for solving the synchronization problem in the actual network system,and has certain reference significance for the research in related fields.