The Dynamics And Control Of Stochastic Multi-agent Systems

For many practical systems,on the one hand,the process of information storage and transmission,is often accompanied by the emergence of the time delay.The stochastic disturbance in the nature,on the other hand,also is inevitable,such as the role of environmental temperature,humidity,wind speed and so on will affect the stability of the system.In order to more accurately describe the dynamic characteristics of the system,design a more suitable control protocol,the model of the system must be fully considered the influence of time delay and stochastic disturbance.This paper is about control problem of the stochastic multi-agent systems with time delay and stochastic disturbance,the main work is as follows:Firstly,almost sure exponential consensus of stochastic second-order multi-agent systems with time delays is studied.The multi-agent systems consider both the stochastic disturbance governed by Bronwian motion and the time delays.First of all,the error dynamic system of second-order multi-agent systems is established.Then by constructing suitable Lyapunov functional and combining with stochastic analysis theory,control technique as well as linear matrix inequality technique,as a result,the sufficient conditions for guaranteeing almost sure exponential consensus of the systems are derived.Last but not the least,simulation examples are presented to demonstrate the effectiveness of the obtained results.Secondly,this paper is concerned with the issue of mean square exponential consensus for second-order multi-agent systems with nonlinear dynamics and external stochastic disturbance.Herein,it is more realistic that the external stochastic disturbance from the change of external environment may have great effect on multi-agent systems.Firstly,by utilizing the graph theory,the stochastic theory,control technique and the linear matrix inequality method,sufficient conditions for guaranteeing the consensus of second-order multi-agent dynamics with external stochastic disturbance are achieved when the digraph of the network is strongly connected.Then,by generalizing strongly connected networks to directed spanning tree networks,the problem of pinning consensus is investigated and the corresponding conditions for ensuring consensus are derived.Additionally,the obtained results are applied to networked Euler-Lagrange systems with external stochastic disturbance and the consensus criteria of networked Euler-Lagrange systems are achieved.Finally,some numerical simulations are presented to illustrate the effectiveness of the theoretical results.Next,this paper is concerned with the passivity problem for a class of Markovian switching complex dynamic networks with multiple time-varying delays and stochastic perturbations.Some sufficient conditions are obtained to guarantee that the complex dynamic networks with multiple time-varying delays and stochastic perturbation under Markovian switching are passive in the sense of expectation.The appropriate stochastic Lyapunov functional was constructed,and stochastic theory,linear matrix inequality technique and properties of Weiner process were employed to achieve the results.Finally,some simulation examples are presented to illustrate the effectiveness of the obtained results.Finally,passivity problem is studied for Markov jump bi-directional associative memory(BAM)neural networks with both mode-dependent mixed time delays and time-varying transition rates.In this paper,we consider both discrete delay and distributed delay which are all switching based on Markov process r(t).Time varying transition rates are,respectively,discussed under the cases of known transition rates and partly unknown transition rates.The mode-dependent time-varying character of transition rates is supposed to be piecewise-constant.By utilizing LMIs technique and a class of Lyapunov functionals,a switching delay passivity criterion underlying known transition rates is derived,which can be easily checked by the Matlab LMI Tool Box.Furthermore,we extend the result to passivity analysis of Markov jump BAM neural networks with partly unknown transition rates.The results obtained relate on not only switching discrete delays but also switching distributed delays.Finally,a numerical example is given to illustrate the effectiveness of the results.