Distributed Dual Optimization Algorithm Of Mutil-agent Systems

In this paper, we study the consensus problem of information communication network system from the viewpoint of the system control theory, which not only helps to reveal the reasons of all kinds of natural population phenomenon and its internal mechanism, but also shows some hints on optimizing the parameters. The obtained results have more practical engineering application. The main work of this paper can be divided into two parts:In the first part of the research, we further study a Push-sum distributed dual optimization algorithm on directed switching network based on the distributed dual optimization algorithm of the Push-sum distributed dual on the fixed undirected network. The conclusion makes use of the notable advantage of Push-sum. It does not require that the adjacency matrix of the network topology is doubly stochastic. The proposed optimization algorithm can still ensure that all individuals can still reach consensus, that is, it finally converges to the true value. Moreover, the objective function of the network is optimal.In the second part, the Push-sum consensus of the switching network with delay in information exchange is studied, and the distributed dual average convex optimization problem is further studied. The existing multi-agent system for distributed optimization algorithm is usually assumed that each individual mutually transmit information in time. However, in practical application, due to packet loss or external disturbance factors, it may lead to delay when individuals exchange information. The paper is based on the Push-sum distributed dual convex optimization. We make the optimization problem with delay into optimization problem without delay through expanding the dimension of the system, and further prove the proposed optimization algorithm with exponential convergence rate without deviation to achieve consensus based on the distributed Push-sum average consensus algorithm, and finally make sure that the objective function on the network achieve the optimum.In summary, in the first part we extended the result of the Push-sum distributed dual average convex optimization for fixed networks to the case of the Push-sum distributed dual average convex optimization for directed switching networks. In the second part, we proved the convergence of for distributed push-sum consensus in the presence of communication delay. Base on the obtained result, we further investigated the distributed dual convex optimization problem with communication delay.