Quantized Consensus Of Multi-agent Systems And Distributed Convex Optimization

In recent years,the optimization problem of large-scale dynamic network system has become a hot research issue.Similar to the traditional centralized optimization problem,it has the characteristics of nonlinear,constraint and so on.In addition,it has the performances of information localization,randomness and asynchronous update of agent's state variables.It also has important applications in many aspects,such as network resource configuration,distributed tracking and positioning,and machine learning in large-scale environment.Among them,distributed optimization of multi-agent systems has a significant effect on solving the problem of coordination and control among agents.In the practical application of multi-agent network problems,there may be many complex situations,such as the limited bandwidth of communication channel among agents,the noise interference in communication process,the cost function is nonsmooth,and there may be a malicious attack on the system.It is significative to ensure that the multi-agent network system is robust and that the system can still run normally in complex situations.In this paper,we mainly study the distributed optimization algorithm and consensus problem of multi-agent network system under complex communication conditions,especially when the communication channel bandwidth is limited.The main research work of this paper is the following two algorithms.The first part is the distributed optimization problem of a sum of convex cost functions with quantized interactions among agents is studied.The network of the agents interacting over a undirected graph,the state information of the agents is transformed into the edge state information between the agents by using the edge laplacian matrix;then the state information of the edges is quantized,and the original cost functions is generated to produce nonsmooth problems,then we select the proper Lyapunov function and introduce the nonsmooth analysis to find the gradient;finally,the algorithm is proved to be uniformly bounded.The second part is the consensus problem,multiple agents of the given system can reach consensus along with the evolution.Recently,research on exploiting the trusted agents to resist the adversary agents of the system has received some attention.Because the existence of the adversary agents,other agents' state information has the risk of leaking,the quantization encryption algorithm is used to protecting agents'privacy.This model is a good approximation for a network of nodes communicating through finite bandwidth channels,so that at each time instant,only a finite number of bits can be transmitted.The algorithm is based on the switching topology,which improves the application of the research.It is proved that all the normal agents and trusted agents will achieve the same value in the final time.In summary,the value of communication information is quantified in the case of the limited bandwidth of communication channel,but quantization leads to a nonsmooth cost function,so nonsmooth analysis is used to solve this problem,and it is proved that the algorithm is uniformly bounded in the system.Due to the presence of malicious interference or attack in the system,by classifying agents and resisting attacks with trusted agents.Besides,the consensus of the algorithm is proved.