Research On Distributed Optimization Algorithm Of Multi-agent System Based On ADMM

In recent years,with the increasing scale of networks,distributed optimization problem has attracted more and more attention in the research of networked multi-agent systems,and gradually developed into a new research hotspot.This paper mainly studies the distributed ADMM-related algorithms based on multi-agent systems,and applies the proposed hybrid ADMM algorithm considering node error and the distributed weighted ADMM algorithm with additional node error to the model predictive control problem.The main research work and conclusions of this paper are as follows:(1)For distributed optimization problem,this paper uses the hybrid communication diagram to unify the centralized ADMM algorithm and decentralized ADMM algorithm.On the basis of the existing work,the distributed ADMM algorithm considering the node error based on the mixed communication graph is derived,and the linear convergence of the algorithm is analyzed.Finally simulation experiments are carried out to test the influence of factors such as the size of the disturbance,the connectivity rate and the number of nodes on the performance of the algorithm,and the convergence of the algorithm and the acceleration performance of the distributed consistent ADMM algorithm with node error are verified.The simulation results show the effectiveness of the proposed analysis in this paper and illustrate the effect of system and network parameters on the performance of the algorithm.(2)In order to solve the distributed optimization problem based on weighted graph,the weighted ADMM algorithm with additional node error is developed based on the above algorithm,and the linear convergence of the algorithm is analyzed.In the simulation experiments,the performance of the algorithm in two kinds of cluster graphs are analyzed by using the edge betweenness centrality as the basis of generating the weight matrix,and the algorithm is tested on the Erdos-Renyi random network.The simulation results show that the weighted hybrid ADMM considering node error and hybrid consensus ADMM algorithm with node error can optimize the decentralized ADMM algorithm with node error,and the weighted algorithm has better acceleration performance,which verifies the effectiveness of the proposed analysis in this paper.(3)The two algorithms derived in this paper are respectively applied to the model predictive control problem,and the distributed ADMM algorithm is applicable through the continuous transformation of the model.The simulation experiments test the performance of the two algorithms in the model predictive control problem,and the simulation results verify the correctness of the theoretical analysis results in the above algorithms.