Collective Behavior And Control Of Multi-Agent Networks

Network science is a new interdisciplinary discipline,whose researchers come from many different disciplines such as physics,mathematics,computer science,statistics and sociology.Interactions between individuals in the network will lead to the emergence of some interesting group phenomena,such as synchronization,phase transformation,swarm and so on.As a very representative network system,multi-agent network has great application prospects in civil and military fields,such as UAV formation,power grid and transportation,etc.Therefore,it has attracted more and more researchers’ attention.Consensus problem is a basic but important topic in the research of multi-agent networks.In this paper,the consensus problem and cooperative control problem of multi-agent network are studied.The main results are as follows:In chapter 2,for multi-agent networks with noise,the consensus problem of multiagent networks induced by multiplicative noise is studied.Firstly,according to the classical consensus model,a stochastic model with multiplicative noise is constructed,and the sufficient conditions for achieving consensus are derived by using the stability theory of stochastic differential equations.Secondly,the effect of noise on the consensus convergence rate is studied in detail.Different from the existing results,it is found that multiplicative noise can promote the realization of consensus.Finally,the results are verified by numerical simulation,and the effect of network topology on the uniform convergence rate is analyzed by using regular networks,small world networks and scale-free networks.In Chapter 3,for leader-following multi-agent networks,we study the finite-time and fixed-time stochastic consensus problem.According to the stability theory of stochastic differential equations,the finite-time and fixed-time consensus protocols are designed.When network topology is undirected,sufficient conditions for finite-time and fixed-time stochastic consensus of leader-following multi-agent networks are given.In the case of a directed network topology,sufficient conditions for achieving finite and fixed time weighted average consensus of leader-following multi-agent network is given.Finally,the theoretical results are verified by numerical simulation,and the effects of network topology and noise intensity on the consensus are analyzed.In Chapters 4 and 5,the time and energy cost for achieving consensus of multiagent networks is studied.Time and energy costs are two important indicators to evaluate the consensus protocols of networking agent systems.Combining the benefits of the linear protocol and finite-time protocol,we propose new switching protocols to solve the finite-time consensus problem of multi-agent networks with undirected and detail-balanced directed topologies.The analytical estimates of time and energy costs are obtained.The results show that time and energy costs depend on the second smallest and the largest eigenvalues of the graph Laplacian,and the control parameters.Especially,we show,both analytically and numerically,that there is a trade-off between time and energy costs,i.e.,reducing the time cost will inevitably increase the energy cost.There are 19 pictures and 122 references in this paper.