Distributed Optimization Of Multi-agent Systems Based On Event-triggered Mechanis

With the development of society,the optimal control of multi-agent systems has a wide range of application value in the fields of optimal energy distribution,sensor networks and so on.So it has attracted the attention of many researchers.Based on the event-triggered mechanism,the distributed optimization problems of multi-agent systems are investigated in this paper.Firstly,considering that communication delays are sometimes unavoidable in multiagent systems,the distributed optimization problem of multi-agent systems with time-varying delays in strongly connected topology is investigated based on the periodic event-triggered mechanism,and a distributed event-triggered zero-gradient-sum algorithm is proposed.Compared with the time-triggered distributed optimization algorithm,this algorithm can reduce the communication load in the networked systems,and has the advantages of low energy consumption and low communication cost.It is also proved that the state of each agent asymptotically converges to the global optimum.Since the event is only checked at the periodic instants,the lower bound of the time interval between two contiguous event-triggered instants is the sampling period and Zeno behavior can be directly excluded.Secondly,considering that in the practical application,dynamic event-triggered can effectively reduce the communication burden between agents.Therefore,using the method of periodic event-triggered,a new event-triggered mechanism is proposed by introducing dynamic variables.The main idea is to realize the dynamic change of the event-triggered threshold by adding auxiliary variables and constructing a dynamic equation.In addition,it is proved that the multi-agent system converges to the global optimum exponentially.Finally,under the event-triggered mechanism,a non-zero gradient sum algorithm based on the proportional-integral strategy is proposed.The zero-gradient-sum algorithm needs special initialization,but the algorithm proposed here can be initialized arbitrarily.According to the La Salle’s invariance principle,the convergence of the proposed algorithm is proved,and Zeno behavior is excluded.