多个体系统分布式对偶优化算法的研究

发布时间：2018-08-22 13:32

【摘要】：文章从系统控制论的角度,对存在信息交流时延的切换网络多个体系统的Push-sum一致性问题进行了研究,同时进一步研究了有时延和无时延两种情形的有向网络分布式对偶优化问题。研究结果不仅有助于揭示各种自然群体现象产生的根源及内在机理,更有助于通过对某些参数来进行优化设计,使其具有更广泛的实际工程应用。本文主要工作共分为以下两部分：第一部分在固定无向网络的Push-sum分布式对偶优化算法的研究基础上,进一步研究了有向切换网络的Push-sum分布式对偶优化算法。所得结论利用Push-sum的显著优势,即它不一定要求刻画网络拓扑结构的邻接矩阵是双随机的,在切换网络周期强连通条件下,所提出的优化算法时仍可保证网络中所有个体仍能达成一致性,即收敛到真实的平均值,且网络的目标函数达到最优。第二部分研究了信息交换过程中存在时延的切换网络Push-sum一致性,并进一步研究了时延情形下的分布式对偶平均凸优化问题。已有多个体系统的分布式优化算法大都是假定每个个体相互之间的信息传递及时、可靠,但在实际应用中,由于数据包的丢失或外界干扰等因素导致网络中个体间的信息传递出现延时的情况。本文是在固定网络的Push-sum分布式对偶凸优化算法的基础上,通过对系统扩维把有时延的优化问题转化为无时延的优化问题,进一步地基于分布式Push-sum平均一致性算法,证明了所提出的优化算法以指数收敛速度无偏差地达成一致性,并确保整个网络的目标函数达成最优。总之,通篇论文主要是把的固定网络的Push-sum分布式对偶平均凸优化算法扩展到有向切换网络的Push-sum分布式对偶平均凸优化算法的研究与证明,第二部分是把具有通信时延的非平衡网络限制一致性用于证明存在通信延迟的非平衡网络的分布式凸优化算法的收敛性上。
[Abstract]:In this paper, from the point of view of system cybernetics, the problem of Push-sum consistency for switched networks with information exchange delay is studied. At the same time, the distributed duality optimization problem of directed networks with sometimes ductility and no delay is studied. The results are not only helpful to reveal the root causes and internal mechanism of various natural population phenomena, but also to optimize the design of some parameters so as to make them more widely used in engineering. The main work of this paper is divided into two parts: in the first part, based on the research of Push-sum distributed duality optimization algorithm for fixed undirected networks, we further study the Push-sum distributed dual optimization algorithm for directed switched networks. The conclusion takes advantage of the remarkable advantage of Push-sum, that is, it does not necessarily require that the adjacency matrix characterizing the topological structure of the network is double random, and under the condition of strongly connective period of switched networks, The proposed optimization algorithm can still guarantee the consistency of all individuals in the network, that is, convergence to the real average value, and the optimal objective function of the network. In the second part, the Push-sum consistency of handoff networks with delay in the process of information exchange is studied, and the distributed dual average convex optimization problem in the case of delay is further studied. Most of the distributed optimization algorithms in multi-individual systems assume that each individual transmits information between each other in a timely and reliable manner, but it is widely used in practical applications. Due to data packet loss or external interference, information transmission between individuals in the network is delayed. In this paper, based on the distributed dual convex optimization algorithm of Push-sum in fixed network, by extending the dimension of the system, the optimization problem with time delay is transformed into an optimization problem without delay, and the distributed Push-sum average consistency algorithm is further based on it. It is proved that the proposed optimization algorithm is consistent with the exponential convergence rate and ensures the optimization of the objective function of the whole network. In a word, the whole thesis mainly extends the Push-sum distributed dual average convex optimization algorithm of fixed network to the Push-sum distributed dual average convex optimization algorithm of directed switched network. In the second part, the limited consistency of unbalanced networks with communication delay is used to prove the convergence of distributed convex optimization algorithms for unbalanced networks with communication delay.
【学位授予单位】：安徽理工大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O157.5;TP301.6

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