The Consensus And Synchronization Problem Of Stochastic Multi-agent Systems

In the real system, the stochastic disturbance is always inevitable. In order to more accurately describe the characteristics of the systems and design better control laws, the system modeling must fully take into consideration the influence of stochastic factors. In addition, the impulsive is also widespread in nature, it is need to take a further step to consider employing stochastic differential equation to describe the system when considering the stochastic perturbation influence on multi-agent dynamic system. In this paper, we investigate the problem of the consensus of the first-order multi-agent system based on stochastic influenced, the main work is as follows:Firstly, impulsive consensus of multi-agent systems with stochastically switching topologies is considered. In this chapter, by utilizing approaches of the stochastic analysis, the impulsive consensus problem for multi-agent systems with stochastically switching topologies is used to study. We propose some sufficient conditions to ensure the multi-agent systems achieving almost surely consensus under the influence of the independent process and Markovian chain, respectively. Finally, the simulation examples verify the validity of our obtained results.Secondly, almost surely exponential consensus of first-order stochastic multi-agent systems is considered. In this chapter, the first-order stochastic systems considered are with external disturbances. There are two protocols to be introduced. One is the system without delay, the other is with the node delay. As the simulation results, the trajectory of each of agents governed by chaotic system powerful confirms the effective of the obtained results.Finally, the mean square stability and exponential stability in mean square of stochastic BAM neural networks with Markovian jump parameters are discussed. Through a suitable Lyapunov-Krasovskii functional established, we give the conditions under which the systems achieve mean square exponential stability. It is not difficult to see that we extend the part of the previous works. The numerical results show the effectiveness of the obtained results and the potential value of application.