Consensus Control And Distributed Optimization Of Multi-Agent System Over Complex Communication Network

In recent years,with the rapid development of science and information technology,multi-agent system has attracted the intensive interest of many researchers and great success has also been achieved.There are many theoretical research methods for analyzing and modeling complex network systems in multi-agent system,and it is also the most important research direction of artificial intelligence.As core research topics of multi-agent system,consensus and distributed optimization of multi-agent system have found wide engineering application in coordination of the distributed sensor networks,demand-response distributed control in smart grids,resource allocation,large-scale machine learning,unmanned-air-vehicle formations,etc.With the growing complexity and scale of networks,it is expected to design more reasonable distributed optimization algorithm and consensus protocol which are capable of facilitating the realistic applications.Based on the above analysis,this dissertation studies distributed optimization and consensus of multi-agent system over complex communication network environments.The major work of the dissertation is organized as follows:(1)The problem of consensus for leader-following multi-agent system is studied in detail.Because the continuous communication transmission between multi-agents inevitably increases the burden of network communication and leads to the great waste of communication network resources,in this dissertation an event-triggered control scheme is introduced to decrease the times of network communication.At the same time,control input with the time delay and leader-following control mode often occur in the factual control,so leader-following consensus protocol with input time delay is designed.This protocol not only alleviates the burden of network communication and computation,but also realizes time delay in actual control while guaranteeing the synchronization of the system.Finally,numerical simulation experiments are given to verify that the system achieves consensus and the number of communications between multi-agents decreases.(2)The problem for consensus of second-order multi-agent system is studied in detail.Considering the limited computational power of multi-agent system,continuous updating of the state will increase the computational pressure.Therefore,we construct a novel consensus control protocol for second-order multi-agent system based on event-triggering control scheme.Assuming that the directed network is strongly connected or contains a directed spanning tree,a new Lyapunov function related to the communication cost and algebraic connectivity is designed,and an algebraic sufficient condition for the consensus of multi-agent system is given.The simulation results show that algebraic connectivity plays an important role in achieving consensus of the multi-agent system.(3)The problem for distributed optimization of multi-agent system based on eventtriggering control scheme is studied.The traditional gradient optimization algorithm uses the diminished step sizes,but it results to slower convergence rate of the algorithm.Also the traditional gradient optimization algorithm requires the assumption of the boundedness of(sub)gradient to ensure the convergence of the algorithm,the condition is very restrictive.We construct the distributed optimization algorithm with incorrect gradient tracking and the heterogeneous constant step sizes.At the same time,there are practical problems such as connection failure,agent failure and communication burden in the network,so event-triggering and asynchronous mechanism are introduced into the algorithm.While the distributed algorithm achieves convergence,it not only realizes the asynchronous communication of agents,but also reduces the waste of communication resources.The simulation results show that the distributed optimization algorithm can geometrically converge to the optimal solution when the heterogeneous step size is less than a certain upper bound.(4)Motivated by potential applications in power systems,we study a problem of convex optimization with a linear constraint on dynamic networks.In practical applications,random link failures occur in complex network and some agents may not work temporally at a certain clock.Therefore,asynchronous implementation is indispensable and typical in the process of computation and network communication.Because the continuous communication transmission between multi-agents inevitably increases the burden of network communication and causes the great waste of communication network resources,we introduce event-triggered control scheme to decrease the times of network communication,and design a new fully asynchronous distributed primal-dual method for this problem.Under two standard assumptions on strong convexity and smoothness of local objective functions,we can achieve linear convergence with the heterogeneous time-varying step-sizes when the heterogeneous constant step sizes are less than an upper bound.Finally,to show the effectiveness of our method we also simulate a number of studies on economic dispatch problems and demand-response problems in power systems.