Fixed-Time Consensus And Flocking Problem Of Multi-Agent

In nature,groups of birds,shoal of fish and foraging ants often show coordinat-ed behavior.The research on coordinated behavior of multi-agent systems has been widely used in engineering and economic fields.The problem of coordinated control of multi-agent systems has become a hotpot in the field of complex networks,which has attracted widely attention from scholars in mathematics,physics,biology and other fields.In the study of coordinated control of multi-agent systems,the convergence speed is a very important aspect and many scholars have conducted a lot of research and exploration on it.The study found that the network structure of multi-agent has an important impact on the convergence speed of multi-agent.So,the researchers tried to improve the convergence speed of the system by optimizing the network structure.At present,most of studies can only guarantee that the convergence of the multi-agent sys-tems is asymptotic convergence,that is,the convergence time is in finite.However,the real system usually can be coordinated within the finite-time.Recently,the problem of finite-time coordinated control of multi-agent systems has attracted attention.Studies have found that the convergence time of the finite-time coordinated control problem depends on the initial state of the system.However,in many practical systems,the ini-tial state is difficult estimate.Therefore,the problem of fixed-time coordinated control has attracted researchers' attention.Multi-agent systems will inevitably be disturbed by environmental noise.Therefore,it is great significance to study the coordinated control of multi-agent systems in noisy environments.Firstly,this paper study the finite-time and fixed-time of multi-agent systems with nonlinear dynamics the problem of time random consensus;then the problem of finite-time and fixed-time flocking of the Cucker-Smale system is considered.The main contents of this article are as follows:1.The introduction part of the paper introduces the research background and progress of the consensus of the multi-agent systems and the flocking problem of the Cucker-Smale system.2.In the second chapter of the thesis,using the finite-time and fixed-time stability theory of differential equations and related results in graph theory,the consensus prob-lem of multi-agent systems with nonlinear dynamics is studied,including:finite-time consensus and fixed-time consensus3.The third chapter of the thesis uses the finite-time and fixed-time stability the?ory of stochastic differential equations to study the finite-time consensus problem and fixed-time random consensus problem of multi-agent systems under noisy environmen-t.4.The fourth chapter of the thesis studies the fixed-time flocking problem of the Cucker-Smale system.Using the fixed-time stability theory of differential equations,we obtain the sufficient conditions for the Cucker-Smale systems to achieve the flock-ing in a fixed-time5.The fifth chapter of the thesis studies the fixed-time random flocking problem of the Cucker-Smale system in a noisy environment.Using the fixed-time stability theory of stochastic differential equations,we obtain the sufficient conditions for the random flocking of the Cucker-Smale system in a fixed-time6.The sixth chapter of the thesis summarizes and looks forward to this articleThere are totaly 12 figures and 85 references in this dissertation.