Research On Flocking And Consensus For Several Kinds Of Multi-Agent Systems

The researches of dynamical behaviour for multi-agent systems(short for systems)play an important role in the fields of UAVs cooperative control,formation control,flock-ing evolution,distributed sensor network,communication congestion control and so on.Consensus problem is a general problem in coordination control of systems,which has become a research hotspot in the field of control science in recent years.In this thesis,flocking behavior and consensus for several kinds of systems were studied by using ma-trix analysis method,fixed point method and Lyapunov method.The models cover from first-order to second-order differential equation,from discrete to continuous systems and the communication weight between agents from constant to function.The main points of the study are as follows:(1)We investigate the consensus problems for discrete first-order and second-order systems with spatial coordinates coupling and processing delay.By using graph theory,difference equation theory and matrix analysis method,the problem of consensus was transformed into the problem of the eigenvalue distribution of system matrix,the neces-sary and sufficient conditions for the consensus of two kinds of systems and the explicit representation of the agent's final state were obtained.The eigenvalues distribution prob-lem was transformed into the polynomial stability problem by bilinear transformation.It was concluded that the two kinds of systems reach a consensus if and only if 0 is a sim-ple eigenvalue of Laplacian matrix and the delay,the step length and the rotation angle are less than the critical value which was determined by the second-order and third-order complex coefficient algebraic equation.The conclusion perfects the theory of systems with time delay.Simulation examples are given to verify the theoretical results.(2)We investigate the problem of group consensus of discrete time first-order and continuous time second-order systems.For the first-order model,by using graph theory,difference equation theory and matrix analysis method,the problem of group consensus was transformed into the problem of the eigenvalue distribution of system matrix,the necessary and sufficient conditions for the group consensus of the first order system and the explicit representation of the agent's final state were obtained.For the second-order model,some sufficient criteria and evolution patterns of group consensus of the systems were derived.When the damping gain is large and the rotation angle is from small to large and crosses the critical value?~c,the multi-agent system will show three flocking patterns:we show that three flocking patterns of systems:linear pattern,cylindrical spiral pattern and logarithmic spiral pattern.The conclusion provides theoretical support for the application of the theory of group systems in many aspects.Simulation examples were given to verify the theoretical results.(3)The Cucker-Smale model(short for C-S model)was modified by introduced multiple time delays,and the flocking characteristics of the processing delay C-S model of systems was obtained.based on the fixed point theorem,we present the existence and uniqueness of the flocking solution for our delayed C-S model when the influence function has the property of Lipschitz and the initial value satisfies certain conditions.At last,we present the asymptotic flocking velocity and the final relative position between agents of the unique flocking solution for such system.It enriches the theoretical results of C-S model and improves the control accuracy for the application of multi-agent system with multiple time delays.(4)We investigate flocking behaviours for two kinds of C-S models with continuous non-Lipschitz protocol.Based on the construction of Lyapunov functional,by using the fixed-time control technology,we show that the flocking can occur in fixed-time when the communication rate function is locally Lipschitz continuous and has a lower bound.Meanwhile,it was proved that when??2,the initial value satisfies certain conditions,and the influence function has singular interval,the system will occur flocking evolution in fixed-time,and the minimum distance between agents in the flocking evolution pro-cess is greater than the control parameter?,which can ensures collision avoiding.The convergence time of C-S model of two kinds of control protocols were independent of the initial speed of the all agents.Simulation examples were given to verify the theoretical results.