Fully Distributed Cooperative Control Of Multi-Agent Systems Under Double-Event-Triggered Mechanism

In the past decades,the cooperative control of multi-agent systems(MASs)is one of the most popular research fields,which usually includes consensus control,containment control,formation control,etc.Due to the limited resources and communication bandwidth carried by the agent,researchers introduced the event-triggered mechanism to reduce the number of control actions to achieve the purpose of saving energy and resources.However,although the controller is not continuously updated,the calculation of triggering conditions still needs the real-time communication with neighbor agents in some studies.In addition,some studies use the estimated state to get rid of the constraint of continuous communication,but the controller needs to be updated at any time.In order to solve the above problems simultaneously,a double-event-triggered mechanism(DETM)is proposed to reduce the resource consumption of communication and controller update,and two triggering conditions are given to determine the instant of communication and controller update respectively.Based on the above ideas,a new DETM is designed in this paper,which can not only reduce the number of controller updates and communication among agents simultaneously,but also solve the problems of consensus control and containment control.The specific works are as follows:1.The containment control problem of linear MASs is studied in this paper.By designing a fully distributed control protocol based on a DETM,each follower can communicate with the neighbor agents or update the controller only at its own triggering instants.The controller is independent of the global information such as the eigenvalues of the Laplacian matrix by adopting the adaptive technique.The generation of the relative state is introduced based only on sampling information,which eliminates the limitation of continuous monitoring of the states of neighbor agents.Based on the above research,this paper extends the problem to solve the situation when leaders’ inputs and followers’ time-varying multiplicative faults as well as additive faults coexist.Finally,it is proved that the proposed controller can realize containment control.With the help of graph theory,matrix analysis,Lyapunov stability,and other theories,sufficient conditions and rigorous proofs are given to ensure the implementation of the controller and the exclusion of Zeno behavior.The effectiveness of the protocol and the advantages of DETM are verified by simulation.2.Considering that containment control can be regarded as a special case of consensus control,the problems are extended to consensus control.The proposed DETM is further improved to a dynamic one,which is the dynamic double-event-triggered mechanism(DDETM).A group of dynamic variables are introduced into each triggering function,which aims to further reduce the energy consumption of communication among agents and controller updates.It is proved that the consensus control is realized under the given sufficient conditions,and Zeno behavior is excluded as well.The effectiveness of the controller and the advantages of DDETM are verified by simulation examples.