Stochastic Consensus Of Multi-agent Systems And Synchronization Of Complex Networks With Pinning Control

The cluster dynamics of complex network systems is an international frontier and hot issue,which has attracted the attention of many scholars.In order to achieve orderly collective behavior in complex network systems,existing studies usually needs to control all individuals.In addition,most of the existing studies ignores the impact of environmental noise on the collective dynamics of complex network systems.This thesis discusses the problem of stochastic consensus and synchronization of complex networks under the influence of noise.Based on the technology of finite-time control and pinning control,the new controllers are designed.This thesis uses graph theory and stochastic differential equation stability theory to give conditions for the network to achieve stochastic consensus and synchronization.The effects of random noise,control parameters,network topology and other factors on the convergence speed are analyzed.The main work of this thesis is as follows:First,the problem of stochastic consensus of second-order multi-agent systems with nonlinear dynamics is investigated.The effect of stochastic noise on the secondorder multi-agent systems is considered,and a new controller is designed in combination with finite-time control techniques.By using the stability theory of differential equations and matrix analysis,the analytical estimation of the upper bound of convergence time is given.Using fixed-time control technique,an effective controller is designed to make the system reach consensus in a finite time and to obtain an estimate of the upper bound on the convergence time independent of the initial state of the system.The effects of factors such as control parameters on the convergence rate of second-order multi-agent systems are analyzed through numerical simulations.Secondly,the stochastic consensus problem of second-order multi-agent systems with pinning control is investigated.The effects of noise and nonlinear dynamics are considered,and combine the advantages of pinning control technique and finite-time control technique,the finite-time and fixed-time pinning controllers are designed to reduce energy costs.The discriminative conditions for achieving stochastic consensus in second-order multi-agent systems are derived.The proposed controller is applied to study the collective behavior of UAV system.The correctness and validity of the theoretical results are verified through numerical simulations.Then,the non-chattering finite-time stochastic cluster consensus problem for multi-agent systems is investigated.A non-chattering finite-time controller is designed for the multi-agent systems under the influence of noise.The controller ensures that the convergence process does not produce chattering problem while the system can achieve stochastic cluster consensus in a finite time.In order to reduce the energy cost,the non-chattering pinning controller is designed using the pinning control technique.Sufficient conditions for the system to achieve stochastic cluster consensus are given and an estimate of the upper bound on the convergence time is given.Finally,the problem of stochastic synchronization of complex networks with pinning control is investigated.Considering the inherent dynamics of individuals,finitetime and fixed-time pinning controllers are designed for the complex network synchronization problem under noise disturbance.Controlling part of individuals to make the network achieve stochastic synchronization in a finite time,and an estimate of the upper bound on the convergence time is given.The effects of the control parameters on the synchronization speed of the network are analyzed using numerical simulations.