Synchronization And Control Of A Complex Delayed Dynamical Network And Multi-agent Systems With Delay And Stochastic Disturbance

As the complexity of the network has become increasingly prominent in real life, the research is alsochanging. Synchronous control of complex dynamic networks and the consistency of multi-agent systemsresearch have touched off a burst of primary wave. Delays and stochastic perturbations are unavailable innetwork transmission. the researches about How to avoid the delay and fluctuation caused during thetransmission of information, and considering the complexity of dynamic network with time delay andstochastic perturbations are a few. As the structure of multi-agent system expanding quickly and thecomplexity continuing deepen, the contacts with the complex dynamic networks are increasingly close. Howto achieve consistent quickly and effectively when the agents have different nonlinear dynamic behavior, thestudy of finite-time consistency has become the focus problem.In this paper, the consistency of time-delay complex dynamic networks with stochastic perturbations andmulti-agent systems have been considered, according to Lyapunov stability of stochastic theory, Ito formula,Kronecker product, graph theory and so on. The following two points have been studied in his paper:(1)The cluster mean square synchronization for a complex dynamical network with interval time-varyingdelays and stochastic perturbation, which is a zero-mean real scalar Wiener process, is investigated. Theweight configuration matrix in the network under consideration is time-varying, which does not need to satisfythe diffusive coupling conditions or be symmetric. According to the stochastic Lyapunov stability theory, It’sdifferential rule, Kronecker product and adaptive control method, an adaptive strategy is established whichguarantees the asymptotical cluster mean square synchronization for each node in the network.(2)The finite-time consensus of a leader-following multi-agent network with non-identical nonlineardynamics and time-varying topologies is investigated. The dynamics of all agents especially the leaders isnon-identical, nonlinear and not only time-related. According to the algebraic graph theory, Lyapunov stabilitytheory and Kronecker product, the control strategy is established which guarantees the finite-time consensus ofmulti-agent network with multiple leaders.Furthermore, several numerical simulations illustrate the effectiveness and feasibility of the proposedmethod.