Research On Distributed Optimization Algorithm Based On Complex Network

Optimization has always been a hot research topic.With the advent of the network information age,distributed systems and distributed computing have attracted more and more attention.This paper mainly studies the distributed convex optimization algorithm of multi-agent system based on complex communication network,and studies undirected topology and directed topology respectively.After a brief introduction of the background knowledge and the concept of preparation,the second chapter studies the event triggered distributed convex optimization problem with time-varying delay and switching topology.The communication between agents is triggered by the conditions monitored by nodes,rather than continuous communication,which can greatly reduce the network burden and reduce the communication cost.In order to solve the optimization problem,by constructing a new Lyapunov-Krasovskii function,a new sufficient condition is proposed to ensure that the state of the agent finally reaches the optimal state,and the upper bound of the maximum allowable delay is given.In addition,it is proved that there is no Zeno behavior in the closed-loop system.Finally,a simulation example is given to illustrate the correctness of the results in this chapter.In Chapter 3,a zero-gradient-sum algorithm with time-varying delays and switching topologies under directed graph topology is proposed.Similarly,the event triggered communication mechanism is adopted,so that the communication between agents is determined by the trigger conditions,and the information exchange can be carried out only when the conditions are met.Using Lyapunov-Krasovskii function method and matrix inequality analysis,combined with the relevant conclusions of directed graph Laplace matrix,a new conclusion is obtained to ensure that the agent state finally reaches the optimal state,and the upper limit of the maximum allowable delay is given.In addition,during the operation of the algorithm,it will be proved that Zeno behavior does not exist.Finally,a simulation example is used to illustrate the correctness of the results.