Event-triggered Consensus For Multi-agent Systems Based On Discontinuous Error Detection

Due to the extensive application value of multi-agent systems,scholars have conducted intensive studies about multi-agent systems and research findings have proliferated in recent years.Consensus problem is a fundamental but critical issue for multi-agent systems,it is a problem in which an appropriate protocol needs to be designed in order to make the states of all agents reach an agreement by the information exchange among agent and its neighbors.Consensus protocols rely on continuous or periodic communication among agents,which will consume a lot of energy.In order to reduce the energy consumption of communication and computing,event-triggered control is applied into multi-agent systems.However,most of the existing results about continuous multi-agent systems require continuous event detection to check event condition,which has no benefit in energy saving.Considering the problems mentioned above,this thesis will study event-triggered mechanism based on discontinuous error detection,an event-based control law is designed to make the system reach consensus.The main contents and results of this thesis are summarized as follows:(1)For a multi-agent system under undirected communication topology,a distributed control protocol which will be updated as the change of a time-varying parameter is designed and the sufficient conditions that the protocol designed can make agents to reach an agreement are deduced.An adjustable threshold parameter which will change with the ratio of the discrete sampling value of error accumulation to the discrete sampling value of error threshold are designed in the threshold function of each agent.Compared with existing research results,the parameter designed in this thesis can be adjusted in the whole process of error accumulation and the increase or decrease trend of the parameter is more compatible with the whole process of error accumulation,which makes the trend can be adjusted to meet different control needs and thus the trigger frequency,or the update frequency of the controller can be changed correspondingly as a result.(2)Taking into account that the accumulation of error is a process,the method that the error of a specific agent is detected periodically within fixed periods can be improved,in that case,event-triggered consensus method with adjustable error detection periods is proposed in this thesis.For a multi-agent system under undirected communication topology,a distributed control protocol which will update as synchronous adjustable periods is designed for each agent,and the sufficient conditions that the protocol designed can make agents to reach an agreement are deduced.The sampling period is dynamically adjusted with the ratio of the threshold to error accumulation in the method with synchronous adjustable periods,and the synchronization of detection instants for all agents can be guaranteed by choosing a common detection period.On the premise that the system can reach average consensus,the method proposed in this thesis can further reduce the communication frequency and the energy consumption of computing compared with the method with fixed detection periods.(3)Based on the consideration that the method with synchronous adjustable detection periods is conservative under certain circumstances,an event-triggered consensus method with asynchronous adjustable error detction periods is proposed.For each agent,a distributed control protocol which will update as asynchronous adjustable periods is designed,and the sufficient conditions that the protocol designed can make agents to reach agreement are deduced.In the method with asynchronous adjustable periods,the periods of error detection can be determined merely by the error accumulation situation of itself and the initial sampling period can be selected arbitrarily,besides,for each agent,a time-varying threshold parameter which can be adjusted with the state of each agent is designed in the threshold function.By using graph theory,matrix theory and other theories,the agreement of the system can be proved under the method with asynchronous adjustable detection periods.The method with asynchronous adjustable detection periods designed in this thesis can effectively reduce the numbers of event detection and reduce the energy consumption of communication and computing,which has better application prospects.