Research On The Prescribed-Time Consensus Control Under Event-Triggered Mechanism

With the continuous development of control science,the control of a single agent can no longer meet the actual needs of life.In this case,the research on the control of multi-agent has become the current research hotspot.In the field of multi-agent cooperative control,the problem of consensus control has always been the focus of research,and the bipartite consensus with cooperative and competitive relationship has also been concerned.In the design of control protocol,the convergence rate is often used as the performance index to evaluate the consensus control protocol.Based on the asymptotic-time consensus theory,some scholars have proposed the finite-time and fixed-time consensus theory which can make the system converge faster.Although the finite-time and fixed-time control protocol improves the convergence rate,its convergence time is still not set by human.In order to meet the actual needs,the prescribed-time control protocol which can preset the convergence time according to the task needs has been paid attention to.In addition,in real life,the huge multiagent system will consume more communication resources,so it is also worth considering to effectively alleviate the communication burden between agents.Therefore,based on the event triggering strategy,in order to improve the convergence rate of the control protocol,this paper studies the multi-agent system including cooperation and competition.The main innovative work is as follows:(1)For the first-order leader-following system with cooperation and competition,in order to obtain the leader’s state,a distributed prescribed-time state observer is designed,so that each follower can obtain the leader’s state estimation in the prescribed-time.In order to improve the convergence rate,a distributed prescribed-time control protocol is designed,so that the follower can complete the two-part consistent tracking of the leader within the prescribed-time after observing the leader’s state.It is worth noting that this chapter uses dynamic event triggering mechanism to more flexibly reduce the occupation of communication resources between agents.Then,it is proved that the trigger time has a strict lower bound,and the system will not produce Zeno behavior by the method of counter evidence.Finally,matlab numerical simulation is used to verify the effectiveness of the prescribedtime observer and controller.(2)For the second-order leader-following system with known leader’s states,a prescribed-time consensus control protocol based on event triggering strategy is proposed.Then,the auxiliary variables are constructed by using the scaling function,and the effectiveness of the proposed control protocol is proved by Lyapunov stability theory.Then,the minimum lower bound of event trigger interval is solved by differential method,and it is strictly demonstrated that the system will not produce Zeno behavior.Finally,the effectiveness of the proposed control protocol is verified by MATLAB numerical simulation of the system.(3)For the second-order leader-following system with competition,a distributed prescribed-time state observer is designed when the leader’s state of the second-order system is unknown.Then the two-part consensus control protocol and event function are designed to ensure that the follower can realize the two-part tracking of the leader within the preset time.Then,the validity of the control protocol is proved by Lyapunov stability theory,and Zeno behavior is excluded.Finally,the effectiveness of the protocol is verified by a simulation example.