Consensus Analysis For Multi-Agent Systems With Stochastic Impulses Under Network Attacks

In the past decades,multi-agent system cooperative control has gradually become a hot research topic in the control science community due to the wide application of multi-agent systems in many fields such as biology,engineering,and artificial intelligence.As a fundamental problem of multi-agent cooperative control,the task of consensus design a control strategy to make all nodes agree on some common goals,so as to accomplish some large-scale clustering tasks.Nowadays,the research on the consensus of multi-agent systems has achieved fruitful results,such as: sampled data-based,output-based,and leader-following-based consensus multi-agent systems.Impulse control is a typical kind of discontinuous control,which has excellent characteristics such as simplicity and flexibility.Meanwhile,compared with continuous control,impulse control can greatly reduce the control cost and network load,so it is widely used in the cooperative control of multi-agent.In the past,many researches have focused on the coherence problem of linear multi-agent systems,and two distributed pulse control protocols have been proposed.Based on this,an improved distributed impulse control protocol for nonlinear multi-agent system is proposed in this paper,and the corresponding consensus criterion is given.It is worth noting that in the existing studies of multi-agent impulse control,the impulse considered are mostly deterministic,i.e.,both impulse intensity and density are assumed to be determined.However,the effect of impulse control in the actual control of multi-agent is often influenced by a large number of stochastic factors.Therefore,stochastic models need to be introduced to characterize the stochastic nature of impulse control.In recent years,a series of important research results on stochastic impulse control have been achieved.However,relatively little research has been conducted on the consensus of multi-agent systems under stochastic impulse control,and there are still many meaningful problems that deserve further study.In addition,the information interaction between individual intelligences through a common network makes multi-agent systems very vulnerable to denial-of-service(Do S)attacks,which by nature prevent data from sensors and controllers from accessing their destinations,and can also be regarded as a special kind of stochastic impulse perturbation.Therefore,studying the consensus of multi-agent under stochastic Do S attacks is certainly a meaningful problem.Based on the above discussion,this paper investigates the consensus problem of nonlinear leader-following multi-agent body system under stochastic impulse control.Firstly,a distributed stochastic impulse control protocol is designed by introducing stochastic parameters to inscribe the intensity of stochastic impulse.Secondly,with the help of probability analysis and Lyapunov function stability analysis,the consensus criterion of leader-following multi-agent under stochastic impulse control is given.The paper is organized as follows:(1)The consensus problem of nonlinear leader-following multi-agent under stochastic impulse control is investigated.Compared with the existing literature,this paper designs a distributed stochastic impulse control protocol in which the impulse intensity is stochastic and the impulse generation frequency is determined by the modally dependent average impulse interval.Using stochastic analysis technique and Lyapunov method,sufficient conditions for the leader-following multi-agent body system to reach agreement under stochastic impulse control are obtained.Also,as a corollary,the consensus criterion for the leader-follower multi-agent system under stochastic denial-of-service(Do S)attack is given in this paper.This paper has some innovations in both system model and research method.(2)The consensus problem of nonlinear leader-following multi-agent with Markov-type stochastic impulse is investigated.Since Markov chains have the property of no memory,they are well suited for inscribing stochastic fluctuations.Compared with the existing literature,this paper introduces discrete-time Markov chains to inscribe the stochastic impulse intensity based on the distributed stochastic impulse control protocol,and uses the average impulse interval to determine the impulse occurrence frequency.Through stochastic analysis technique,sufficient conditions for nonlinear leader-following multi-agent to reach consensus are obtained.Due to the introduction of discrete-time Markov chains,the conclusions of this paper can be more general as the existing results related to stochastic impulse control can be considered as the special case of this paper.