Fixed-Time Consensus Of First-Order Multi-Agent Systems

As one of the fundamental problems in the cooperative control of multi-agent systems,consensus has attracted extensive attention from researchers due to its broad applications in unmanned formation control,environment monitoring,vehicle control and so on.Following the existing results,fixed-time consensus of first-order multi-agent systems is considered in this dissertation.The main contributions of the dissertation are as follows:1.Fixed-time consensus is studied for first-order linear multi-agent systems over signed directed graphs.Fixed-time control protocol is firstly proposed.Then,Lyapunov stability theory is used to derive the sufficient conditions for fixed-time consensus by using the inequality technique.The upper bound of the convergence time is also provided,which is independent of the initial conditions of the systems.Finally,numerical simulations are performed to verify the validity of the theoretical results.2.The fixed-time consensus problems of first-order linear and nonlinear multi-agent systems with disturbances are investigated,respectively.Firstly,consensus protocols are proposed.With proposed protocols,it is proved that the states of all agents can achieve consensus within fixed time if the control parameters satisfy certain conditions.Finally,simulation examples are provided to verify the effectiveness of the theoretical results.3.The fixed-time bipartite consensus problem is investigated for first-order multi-agent systems over signed directed graphs.To reduce the energy consumption in the control process,a distributed event-triggered control protocol is proposed.Graph theory and Lyapunov theory are utilized to derive the sufficient conditions for fixed-time bipartite consensus.The upper bound of the convergence time is also provided.In addition,it is shown that the proposed event-triggered control scheme can avoid the continuous control of the agents and the Zeno behavior effectively.Numerical examples are provided to verify the validity of obtained results.