Distributed Subgradient Optimization Algorithms For Multi-agent Switched Networks

In recent years,with the development of complex system science,many distributed algorithms can be implemented by means of multi-agent system.Because many centralized algorithms are difficult to solve the optimization problem of complex systems,the research on distributed algorithms has drawn more and more attention.At present,distributed optimization algorithm has been widely used in all aspects of human life,such as information storage and transfer among banks and other financial institutions,scheduling of urban traffic,Internet network,formation flying of cluster UAV,coordination and so on.In short,the multi-agent system is a large-scale networked system which is composed of a large number of autonomous individuals coupled through local information transmission.Each individual in the network has the ability of autonomous decision-making and calculation and coordination through information transfer with neighboring neighbors to complete complex tasks.Compared with the centralized algorithm,the distributed algorithm has the advantages of not needing global information,having strong robustness and adaptability under complicated environment,and saving cost and pay more attention to the important role that communication and individual coordination play in optimizing.Therefore,this paper studies from two aspects of the network topological conditions of multi-agent system and the communication between individuals.When multi-agent system operate in harsh environments,the exchange of information between individuals in the system becomes very difficult or impractical due to the emergence of data packet loss,link failure,or different perception ranges of individuals.Therefore,it is of great practical significance to study non-reciprocal information communication among individuals in multi-agent system.In addition,Most of the existing distributed algorithms are generally based on an idealized assumption that the individuals communicating in the network of the system communicate exactly the information of each individual's state variables.This means that the information channel in the network requires infinite bandwidth and the algorithm can be executed with infinite precision.This means that the information channel in the network requires infinite bandwidth and the algorithm can be executed with infinite precision.Due to the fact that the networked multi-agent systems are spatially distributed in nature and the limited bandwidth limits exist between the information channels connecting the system individuals,this results in the actual systems being able to communicate based on quantitative information rather than accurate information.Therefore,this paper first studies the general distributed unconstrained convex optimization in switched networks with unbalanced networks.Furthermore,considering network topology and quantization information communication,the distributed unconstrained convex optimization problem of directional unbalanced switching network based on quantitative information communication exchange is emphatically studied.The main contents of the thesis and research results are summarized as follows:First,this paper study the distributed sub-gradient optimization algorithm for directed unbalanced switching networks.Different from the assumption of idealization in the literature,it is assumed that the directed network topology must be balanced,which means that the exchange of information among individuals in a multi-agent system is balanced.And this condition is too harsh in practical application.Because of the multi-agent system has the characteristics of spatial distribution,individuals usually share information based on remote communication and wireless sensor network.In particular,the network running in a very harsh environment,often resulting in a systematic network of individuals between the communication network is directional unbalanced.Therefore,considering the strongly connected directional unbalanced switching network,the requirements of the actual network topology conditions are reduced and the applicable range of the existing literature algorithms is expanded.Since the adjacency matrix of the unbalanced network is random,it is difficult to analyze the distributed subgradient optimization algorithm of the unbalanced switched network by using the transition matrix method.In this paper,Under the condition that the directional unbalanced switched network is strongly periodic and the corresponding adjacency matrix is random rather than double random,it is proved that the convergence of the distributed subgradient optimization algorithm for directional unbalanced switching networks by the non-quadratic Lyapunov function method.Compared with the existing distributed subgradient optimization algorithm with directed balanced network,both algorithms converge to the neighborhood of the optimal value in the directed unbalanced switching network and the convergence rates are almost the same.However,obviously,The proposed distributed subgradient optimization algorithm has a smaller iterative error.The simulation examples are given to verify the effectiveness of the proposed algorithm.Second,the finite-level dynamic consistent quantification strategy is used to study the general unconstrained distributed convex optimization problem of directed unbalanced switched networks.If the individuals that make up the network communicate the exact information of each individual state variable,in other words,if the state variable being transmitted is a real-valued situation,the actual network information channel is required to have an infinite bandwidth and the algorithm can be executed with infinite precision.This leads to the fact that in real networked systems,the impossible communication between individuals is completely accurate information.Considering the directional unbalanced switching network,individuals exchange information through quantitative information of an individual state variable and the information transmission is limited by the bandwidth of the wireless communication network,the paper presents a distributed quantization subgradient optimization algorithm for directional unbalanced switching networks.Therefore,considering the network topology conditions and quantitative information communication,it is more practical to weaken the existing literature on the assumption of the adjacency matrix characterizing the network topology and the requirements on the network bandwidth.It is proved that the convergence of the distributed quantization subgradient optimization algorithm proposed in this paper is based on the non-quadratic Lyapunov function method.Finally,the simulation example shows the effectiveness of the algorithm.The simulation results show that no matter how large the size of the network is,the algorithm does not require additional communication costs for communication feedback and reduces the network overhead under the same condition of network bandwidth,all individuals need to achieve the same amount of information,cost savings.And make individuals in multiple system systems network converge faster,thus reducing the unlimited dependence on network bandwidth.In summary,This paper proves the convergence of the distributed subgradient optimization algorithm for directional unbalanced switched networks under the condition that directional unbalanced switching networks are strongly periodic and the corresponding adjacency matrix is random rather than double random and subgradient bounded.And assuming that all information is quantized by a uniform quantizer with finite quantization level prior to transmission,it proves the convergence of the distributed quantization subgradient optimization algorithm for directional unbalanced switching networks.The research shows that compared with the distributed subgradient optimization algorithm with directed balanced switching network,the distributed subgradient optimization algorithm with directed unbalanced switching network weakens the requirements of the network topological conditions and has smaller iterative error.Distributed quantitative Subgradient optimization algorithm for directed unbalanced switching network by selecting parameters of a finite level dynamic consistent quantizer,the network cost can be saved and the reliance on network communication bandwidth can be reduced.Therefore,the distributed subgradient optimization algorithm proposed in this paper has a wider scope of application and application value.