Event-triggering Design And Synchronization Anlysis For Multi-agent Systems

Event-triggered control is a new emerged sampled-data control method that outper-forms the time-triggered control in terms of saving limited control resources and reliving communication burdens.In the multi-agent system,agents are required to interact with neighbors so as to achieve the global objective of the overall system.However,the agents are usually large-scaled and distributed in a wide region,and thus the efficient usage of control resources has attracted great attention in multi-agent systems.In recent years,the event-triggered control for multi-agent systems has become a hot research topic since it is an alternative strategy to solve these resource restriction problems.Many challenges in the design of distributed event-triggering condition and theoretical analysis arise from the underlying communication topologies of multi-agent systems.Moreover,the event-triggered systems belong to a class of hybrid systems and the analytical tools for such systems are far from being completed.Based on the existing work in the event-triggered control,this paper devotes to proposing new event-trigged control designs and developing new analysis methods for multi-agent systems.The main contributions are listed as follows:The edge event-triggered consensus control for multi-agent systems with single-or double-integrator dynamics under directed communication topologies is investigated.With the edge event-triggered sampling strategies,we propose a class of novel consensus protocols to reduce the frequency of controller updates.The main features of the proposed edge event-triggered control include three aspects:(i)the measurement error is defined according to directed information flow and thus it allows that the communication topology is directed,(ii) each individual controller update its edge states only when the associated edge event occurs and the control actions are independent of each agent,and(iii) the proposed edge event-triggered control does not exhibit Zeno behavior.By graph theory and matrix analysis,the consensus conditions are established for the multi-agent systems with single-or double-integrator dynamics underlying the directed communication topologies with spanning trees.The synchronization problem of coupled harmonic oscillators is addressed by event-triggered control.Based on node states,a centralized event-triggered control strategy is first developed and is further extended to a decentralized counterpart,in which the control protocol and event-triggering conditions only require local information.With the node-based event-triggered control strategies,controllers update at the discrete instants when the related measurement errors exceed some proper state-dependent thresholds,which can reduce the computation costs of controllers.By the tools from nonsmooth analysis,it is shown that the proposed event-triggered control strategies synchronize all oscillator states asymptotically.Furthermore,a decentralized event-triggered strategy with a fixed thresh-old is proposed for the sake of excluding the Zeno behavior.Based on the formulation of edge dynamics with respect to two coupled oscillators,we propose a new edge-based event-triggered control strategy to address the synchronization problems of coupled harmonic oscillators.Combined with the periodic event-detecting and edge event-triggered approach,sufficient conditions that guarantee the synchronization of coupled harmonic oscillators are presented.Two edge event-detecting rules are given to achieve the synchronization of coupled harmonic oscillators with low resource consumption.The synchronization problem of Kuramoto oscillators under sampled-data updating law is considered.This study is motivated by the needs of synchronization of Kuramoto oscillators in the presence of intermittent and asynchronous coupling updates.Based on the periodically sampled-data method,a sufficient condition ensuring synchronization under periodic updates is derived.In order to relax the requirement of having all data updated simultaneously,an event-triggered law is designed to implement asynchronous coupling updates.Our synchronization analysis does not rely on any linearization technique around equilibrium points and the mean field theory,instead,we propose a new Lyapunov function based on the edge states and employ the nonsmooth analysis technique to deduce the synchronization conditions.The distributed output synchronization problem of heterogeneous discrete-time nonlinear multi-agent systems with input shortage passivity is studied.In order to reduce the communication burden and the update frequency of controllers,an event-triggered distributed synchronization protocol is proposed where the transmission of output states and the updates of controllers are only needed at event instants.By using the passivity-based control,we show that the multi-agent system can be driven to output state synchronization provided that the coupling strengths are weak enough.