Distributed Optimization Of Multi-Agent System Over Complex Communication Environment

In recent years,with the continuous progress of science technology and sensor networks,more and more researchers have paid their academic attention to multi-agent system and have obtained many remarkable achievements.On the one hand,multi-agent system provides a theoretical research method for modeling and analyzing complex systems.On the other hand,multi-agent system is also the important branches of distributed artificial intelligence research.As one of the most essential research subjects of multi-agent system,distributed optimization of multi-agent system has attracted intensive research interest over the past few years due to their wider applications in distributed formation control,cloud computing,distributed data fusion,information processing and wireless sensor network,etc.With the increasing scale and complexity of networks,it is expected to design some more reasonable distributed optimization strategies to deal with practical application.Based on the observation,this dissertation focuses on more practical distributed optimization problems,i.e.,distributed optimization of multi-agent system over complex communication environments.The main work of this dissertation is summarized in the following three aspects:(1)The problem of distributed optimization for multi-agent system over time-varying unbalanced directed network topologies is studied.Traditional distributed(sub)gradient-based optimization algorithms usually require a perfect synchronization mechanism and a decaying step-size for achieving the exact optimal solution,restricting it from being asynchronously implemented and resulting in slower convergence rate.In addition,the assumption of the boundedness of(sub)gradient is often made for convergence analysis,which is quite restrictive in unconstrained optimization problems.Therefore,a novel distributed optimization algorithm is presented,which combines the distributed inexact gradient tracking technology.At the same time,it is also pointed out that the proposed algorithm is applicable to both time-varying unbalanced directed networks and uncoordinated constant step-sizes.Under the conditions that the objective function is strongly convex and has Lipschitz continuous gradient,we establish the selection criterion of uncoordinated step-sizes and the analysis criterion of performance of the algorithm.Theoretical analysis shows that the distributed algorithm is capable of driving the whole network to geometrically converge to an optimal solution of the convex optimization problems as long as the uncoordinated step-sizes do not exceed some upper bound.An explicit analysis for the convergence rate of the proposed algorithm is also given through a different approach.Finally,simulation results illustrate the effectiveness of the proposed algorithm and the correctness of the theoretical analysis.(2)The problem of distributed optimization of first-order discrete-time multi-agent system based on event-triggered communication is studied.On the one hand,the direct and continuous information transmission of the agent will inevitably increase the pressure on the network communications and cause the waste of communication resources.On the other hand,agents' computation is limited,continuous updates will increase agent' computing pressure.Therefore,distributed optimization algorithms based on continuous communication do not have good practical value,and its related theoretical results can not guide the practical application well.We incorporate event-triggered communication mechanism into distributed optimization over first-order discrete-time multi-agent system.By designing high performance event-triggerred functions and incentive conditions,the distributed optimization of multi-agent system is realized under the conditions of limited network communication resources and agent computing resources.We construct a novel analysis framework of event-triggered distributed optimization over multi-agent system,and establish the analytical relationship between communication cost and the parameters of the proposed algorithm.Finally,simulation results illustrate the effectiveness of the proposed algorithm and the correctness of the theoretical analysis.(3)The problem of distributed constrained optimization for multi-agent system based on asynchronous broadcast communication and asynchronous update strategy is studied over an unbalanced directed network topology.In practical applications,networks are easily susceptible to certain random link failures and a slice of agents may not do any operation temporally at a certain clock.Therefore,asynchronous implementation is typical and indispensable in the process of communication and computation.We mainly concentrate on an epigraph form of the original constrained optimization to overcome the unbalancedness of directed graphs,and propose a new distributed asynchronous broadcast-based algorithm.Unlike other methods,our algorithm guarantees that at every iteration each agent performs an optimization step of its local objective function and local constraints followed by a dynamical averaging of itself and its in-neighbors.The proposed algorithm allows not only updates of agents are asynchronous in a distributed fashion,but also step-sizes of all agents are uncoordinated.A striking feature of the proposed algorithm is that it can deal with the constrained optimization problems in the case of unbalanced directed networks whose communications are subjected to random link failures.Under two standard assumptions that the communication network is strongly connected and the(sub)gradients of all local objective functions are bounded,an explicit analysis for convergence of the algorithm is provided.Simulation results on a numerical experiment are demonstrated to substantiate the feasibility of the proposed algorithm.