Distributed Optimization Algorithm For Multi-agent System And Its Application

In recent years,with the rapid development of science and technology,the network systems are developing towards to large scale,high complexity and high intelligence,and the components of the system are further transformed from controlled objects with single function to agents integrated with the capacities of certain sensing,communication,computing and execution.These reforms and developments in the field of network systems eventually contributed to the present complex system theory.Influenced by this,the theory of multi-agent system emerges as the time requires and becomes an important theory in solving complex system problems.When facing to dynamic and open environment optimization problems,the traditional centralized method is unable to effectively solve the practical application.While distributed method is characterized by its high tolerance of fault,self-organization and scalability,and it can effectively solve this kind of optimization problems which have more realistic background and significance.Many researchers begin to turn their attention to distributed theory,and the reason is that distributed optimization for multi-agent systems have been widely used in sensor networks,signal processing,resource allocation,smart grid and other engineering fields.With the continuous development of its application fields,it is expected to design some more distributed optimization algorithms with high-performance to meet various practical needs in reality.Therefore,in order to design some distributed optimization algorithms for dealing with the problem with certain engineering background,this paper mainly focuses on weakening related conditions of existing algorithms.The main work of this paper can be divided into the following three parts:The first part deals with general unconstrained distributed optimization problems.Under the assumption that the undirected time-varying communication networks are uniformly connected,a distributed optimization algorithm based on the inexact gradient tracking method is designed to solve the practical convex optimization problem,and several important factors,such as time-varying network topology,time-varying uncoordinated constant step-sizes and convergence rate,are considered in this algorithm.Meanwhile,when the conditions of the objective function change convex and coercive to strong convex,the convergences and convergence rates of this algorithm are analyzed and established in this paper.Finally,simulation results indicate the effectiveness of the proposed algorithm and the correctness of theoretical analysis.The second part focuses on the distributed optimization problems with equality constraints and inequality constraints.A distributed optimization algorithm based on random sleep scheme is designed to solve the dispatch response problem in power systems over stochastic networks.Theoretical analysis shows that this algorithm still can expectantly converge to its optimum solution for the stochastic networks with link failure,and the range of uncoordinated constant step-sizes is clearly established in this paper.At the same time,the train of thought behind this algorithm is systematically introduced.Finally,the simulation results illustrate the feasibility of the proposed algorithm.The third part continues to focus on the distributed optimization problems with equality constraints and inequality constraints.A distributed optimization algorithm based on stochastic gradient is proposed to solve the economic dispatch problem with communication delays over directed network which considers the influence of gradient noises and communication delays on the algorithm.Although there exist noise and communication delays over directed network,theoretical analysis shows that the proposed algorithm still can expectantly converge to its optimum solution at a fast rate.The train of thought behind this algorithm is systematically introduced,and its convergence rates is clearly established.The simulation results show the effectiveness of the proposed algorithm.In summary,this paper focuses on solving the distributed optimization problems without constraints or with equality constraints and inequality constraints.This paper provides new ideas for designing more reasonable distributed optimization algorithms,which can be used for reducing the consumption of the communication resources,relieving the pressure of computation for the network,and extending the operating life of system.