Finite-Time Consensus For Second-Order Multi-Agent Systems

Multi-agent systems complete the work through cooperation and coordination among agents.Compared with the traditional control systems,multi-agent systems can reduce the complexity of task and has advantages of high flexibility and reliability.The consensus problem is the basic of research on multi-agent systems and increasing convergence rate becomes the focus of many researchers.Finite-time consensus means that under the appropriate control protocol,all agents can adjust their own states according to local information to achieve the same state in a finite time.Therefore,this thesis mainly focuses on finite-time consensus problem of second-order multi-agent systems,and the main contents are as follows:1.We study the finite-time lag-consensus problem for multi-agent systems under directed topology.Lag consensus refers to the fact that followers track the leader's state trajectory with a time delay in order to avoid congestion.The control algorithm with finite-time term is presented for multi-agent systems without and with disturbance,respectively.By Lyapunov theory,we can get the conditions for reaching lag consensus in finite time.Finally,the validity of the results is verified by numerical simulation.2.Under the condition that the control input has constraint,the consensus control problem for second-order multi-agent systems with undirected topology is considered.Firstly,the finite-time consensus problem for systems with fixed coupling weights is studied.Based on the homogeneous theory,the control protocol and corresponding theoretical proof are given.Then,the asymptotic consensus problem is studied when the coupling weights are unknown.The coupling weights in the control protocol are optimized by using the distributed adaptive control method,and the theoretical proof is given by Lyapunov theory.Finally,the controller of finite-time consensus combined with adaptive feedback control is given and compared with the previous results by numerical simulations.