Research On Distributed Optimization Method For Multi-agent System

In the last few years,the research on distributed optimization problem has been emerged swiftly with extensive applications(i.e.,large-scale networks,distributed estimation,distributed source localization).The optimization problem is usually modeled as minimizing the sum of all the agents' cost functions and it is closed related to many applications in a variety of problems such as sensor scheduling,tracking,distributed optimal power flow,containment control,distributed optimal source allocation,regression of distributed data,etc.In particular,recently the distributed optimimization algorithms have also much applied to solve the economic power dispatch problem or the social welfare maximization problem in smart grids.In multi-agent systems,each distinct agent is assigned with a local cost function.The objective of multi-agent systems is to solve the global optimization problem by the cooperation within multiple agents in a distributed manner.Although domestic and foreign experts and scholars have made fruitful achievements in this field,there are still many unsolved problems worth further studing.Based on these facts,this dissertation deeply investigates the distributed optimization for the first-and second-order multi-agent systems with or without the presence of disturbance and communication delay.Moreover,the problem of reducing communication costs and energy consumptions is also considered for the real-time applications.With the design of the Lyapunov function,the help of convex analysis,internal model principle,Lyapunov stability theory for time-delay systems and LaSalle's invariance principle,the criteria about the selection of controller parameters are derived to ensure the proposed algorithms converge to the optimal solution of the optimization problem with or without the presence of disturbance and communication delay.The main contents of this dissertation are listed as follows:For first-order multi-agent systems,the distributed optimization algorithm is proposed to achieve the optimization of first-order multi-agent systems with the simultaneous presence of external disturbance and the communication delay.In fact,the influence of disturbance or the impact of communication delay has been discussed in existing works on the first-order multi-agent systems.However,the simultaneous influence of disturbance and communication delay is neglected.In this dissertation,the controller has been designed to handle the simultaneous influence of disturbance and communication delay.This proposed controller has a simpler structure compared with the existing controller.Moreover,the conditions are derived for the slowly and fast varying delay,respectively,to ensure the algorithm converging to the optimal solution.For second-order mutil-agent systems,the distributed optimization algorithms using position-only interaction are proposed,which is different with the existing distributed optimization algorithms.This can reduce communication costs,as well as be relatively easy in application compared with these algorithms utilizing the relative velocity information of neighbors.Moreover,to handle the influence of disturbance and communication delay,the distributed optimization algorithms for second-order mutil-agent systems with the presence of external disturbance and communication delay are proposed repectively.Based on the internal model principle,a sufficient condition for solving the distributed optimization problem of double-integrator systems is derived to guarantee that optimization can be obtained regardless the presence of external disturbance.Furthermore,based on the Lyapunov stability theory for time-delay systems,the delay-dependent conditions are derived for the slowly and fast varying delay,respectively,to ensure the algorithm converging to the optimal solution of optimization problem.In addition,from the relationship between the discrete-time control signal and the control algorithm of fast varying delay,a discrete-time communication scheme is also proposed,which can significantly reduce the number of communications in the network.In real-time applications,the power source of each agent and the bandwidth of communication network are inevitably limited.In view of this aspect,to reduce the communication costs,this dissertation proproses two distributed optimization algorithms for the second-order multi-agent systems with event-triggered and time-triggered communication,respectively.These proposed distributed algorithms use position-only interaction and will greatly reduce the communication costs,by avoiding the continuous-time interactions with neighbors.This is different from the existing works on the second-order multi-agent systems.Finally,several numerical examples are presented to illustrate the effectiveness of proposed distributed optimization algorithms.