Research And Application On Distributed Optimization Algorithms Over Multi-agent Systems

With the rapid development of science and technology and the continuous expansion of the network scale,traditional centralized control and optimization techniques have been difficult to solve large-scale complex network problems.Distributed optimization algorithms with more robustness and flexibility have received increasing attention.In view of the irreplaceable advantages of multi-agent systems in distributed computing,many researchers use it as a carrier of distributed optimization for theoretical research and application promotion.Distributed optimization theories of multi-agent systems have been widely applied to scientific research,engineering applications and various aspects of social life,such as wireless sensor networks edge coverage and source location,traffic congestion control,multi-robot formation control,and power resource allocation,etc.The distributed optimization of multi-agent systems achieves the global optimization goal through the interaction and cooperation of multiple agents.The global objective function is the sum of the local objective functions of all agents,and each local objective function is uniquely known by a single agent.Based on the existing research,the related theories are further enriched,and some more general distributed optimization algorithms are proposed to solve the optimization decision-making problems in real life.The main research contents are summarized as follows:(1)For distributed optimization problems over directed graphs,we summarize the existing distributed first-order methods and propose a novel distributed optimization algorithm based on first-order methods.Under the assumptions that the local objective function is strongly convex and Lipschitz continuous,the proposed algorithm ulitizes row-stochastic matrices and uncoordinated step-sizes,which accurately drives each agent gradually converge to a global optimal solution.We overcome the imbalance caused by the directed graph by introducing an auxiliary variable.In addition,the momentum parameter is introduced into the algorithm,which greatly improves the convergence rate of the algorithm.We demonstrate that the proposed algorithm achieves linear convergence when the maximum step-size and momentum parameters do not exceed the given upper bound.Finally,the correctness of the theoretical analysis is proved by the simulation experiments,and the performance comparison results of the related algorithms are given to show the superiority of the proposed algorithm.(2)The economic dispatch problems in smart grid over time-varying balanced directed communication networks is studied,which aims to minimize the total cost of power generation.This kind of economic dispatch problem can be regarded as the optimization problem dealing with the sum of local objective functions.Each agent only has its local objective function,and the constraints of the agent variables are composed of global coupling equality constraints and local linear constraints.For such problem,we design a fully distributed primal-dual optimization algorithm with time-varying uncoordinated step-sizes.In consideration of saving computing and communication resources,the event-triggered scheme is introduced into the distributed algorithm.Each agent can only exchange information with neighboring agents at some independent event-triggered sampling time,which effectively reduces the number of agents' updates and the network burden.Under the assumptions that strong convexity and smoothness of the local objective function,the algorithm linearly converges to a global optimal solution,and the Zeno-like behavior is rigorously excluded.Finally,effectiveness of the algorithm and correctness of the theoretical analysis are verified by numerical experiments.In summary,we focus on the related research on distributed optimization theories and applications over multi-agent systems,which aims to reduce the communication resource waste and relieve the computational pressure.The research results further enrich and develop the existing distributed optimization theories,and provide important theories and key technologies for solving the distributed optimization problem in the practical system.