Consensus Of Multi-agent Systems Under Complex Network

Recent years,the cooperative control of multi-agent systems has drawn increasing attention because of its broad applications in engineering fields such as virtual reality,intelligent robots,wireless sensor networks,and unmanned aerial vehicles formation flying.As one of the most fundamental problems in cooperative control,the consensus problem has even attracted more attention from researchers.The key goal of consensus control is to design a distributed consensus protocol so that agents can reach a common state by local communication.In the actual environment,time delay,disturbance,packet loss,and dynamic communication topology may limit the communication between agents,thereby affecting system performance and destroying system stability.Therefore,in order to improve the convergence performance and anti-interference ability of the system,it is of theoretical and practical significance to design more effective consensus protocols under complex network.Considering the factors such as probabilistic time delay,switching topology,heterogeneous dynamics,leader-following consensus,this paper studies the consensus problem of multi-agent systems under complex network.The main contents are as follows:1.Mean square consensus of heterogeneous multi-agent systems with probabilistic time delay under fixed and switching topology is studied,including leader-following and leaderless cases.In this problem,considering the intermittent occurrence of delay,a Bernoulli random variable is introduced to describe the occurrence probability of delay.Moreover,the multi-agent systems consists of first-order and second-order agents.Firstly,according to the designed control protocol,the dynamics of the state error vector of the heterogeneous systems is obtained.Then,by selecting an appropriate Lyapunov function and using stochastic theory,sufficient conditions that guarantee the mean square consensus of heterogeneous systems are established in the form of linear matrix inequalities.Finally,the effectiveness and applicability of the proposed control protocols are validated by numerical simulations,and the relationship between the occurrence probability and the maximum allowable upper bound of the delay is given.2.Mean square consensus of first-order multi-agent systems with multiple probabilistic intervals time delay under fixed and switching topology is studied,including leader-following and leaderless cases.In this problem,considering that some values ofdelay are very large,but the probability of its occurrence is very small,multiple random variables obeying the Bernoulli distribution are introduced to describe the probability of the delay taking values in multiple intervals.Firstly,according to the designed control protocol,the dynamics of the state error vector of the first-order system is obtained.Then,by constructing a suitable Lyapunov function and using some integral inequalities,sufficient conditions that guarantee the mean square consensus of required systems are derived.Finally,the correctness of the theoretical results was verified by numerical simulations.