Non-Flocking And Finite-Time Consensus Of Second-Order Multi-Agent Systems

Due to the widespread applicable areas of multi-agent systems,it has attracted lots of attention.In this paper,we investigate the non-flocking and flocking for the Cucker-Smale model with distributed time delays and finite-time consensus of leaderfollowing second-order multi-agent systems.The main studying contents of this paper are as follows:(1)For the Cucker-Smale model with distributed time delays,based on the definition of flocking behavior and by establishing and appropriately estimating an inequality of the position variance such that the second order space moment is unbounded,we drive a sufficient condition for the non-existence of the asymptotic flocking when the time delays satisfy a suitable smallness assumption.Furthermore,we also provide a sufficient condition of asymptotic flocking.It is helpful to solve the flocking behavior problem of multi-agent system under imperfect communication conditions.(2)For leader-following second-order multi-agent systems,assuming that the undirected weighted graphs are connected and there is at least one agent i such that pi > 0,by constructing a delicate Lyapunov function,the finite-time consensus is established for very general protocols and topologies.On the one hand,the topologies of position communication and velocity communication(as well as the pinning control inputs for velocity and position)are independent.More importantly,the exponents of velocity and position only need satisfy that β > α.(3)Based on the above work and the differences between the leader and followers,this paper design the leader-following protocol which the leader and followers have different nonlinear factors.We design a leader-following finite-time consensus protocol in which the leader and the follower have different nonlinear factors.Assuming that the undirected weighted graphs are connected and there is at least one agent can receive the leader’s information,we obtain the finite-time consensus of the leader-following second-order multi-agent system with the same nonlinear factors of position and velocity.We also consider the finite-time consensus of the leader-following second-order multi-agent system with the different nonlinear factors of position and velocity.