求解大型线性系统的K-均值最大残差块方法

求解大型线性系统,带K-均值聚类的贪婪随机块Kaczmarz方法是近几年被广受关注的一类方法。本文在该方法基础上做了进一步的研究即在每一次迭代中优先消除残差向量中的最大块,构建了最大残差块Kaczmarz方法及其加速版本并进行了收敛性分析。数值实验证实了本文算法的有效性。The greedy random block Kaczmarz method with K-means clustering for solving large linear systems has been widely studied in recent years. This article conducted further research on this method by prioritizing the elimination of the largest block in the residual vector in each iteration, constructing the Kaczmarz method for the maximum residual block and its accelerated version, and conducting convergence analysis. Numerical experiments have confirmed the effectiveness of the algorithm proposed in this paper.

On a Matrix Equation AX+XB=C over a Skew Field

In this paper we study a matrix equation AX+BX=C(I)over an arbitrary skew field,and give a consistency criterion of(I)and an explicit expression of general solutions of(I).A convenient,simple and practical method of solving(I)is also given.As a particular case,we also give a simple method of finding a system of fundamental solutions of a homogeneous system of right linear equations over a skew field.

The New Architecture with Time-Spatial Consistency for 5G Networks

While operators have started deploying fourth generation(4G) wireless communication systems,which could provide up to1 Gbps downlink peak data rate,the improved system capacity is still insufficient to meet the drastically increasing demand of mobile users over the next decade.The main causes of the above-mentioned phenomenon include the following two aspects:1) the growth rate of the network capacity is far below that of user's demand,and 2) the relatively deterministic wireless access network(WAN) architecture in the existing systems cannot accommodate the prominent increase of mobile traffic with space-time domain dynamics.In order to address the above-mentioned challenges,we investigate the time-spatial consistency architecture for the future WAN,whilst emphasizing the critical roles of some spectral-efficient techniques such as Massive multiple-input multiple-output(MIMO),full-duplex(FD)operation and heterogeneous networks(HetNets).Furthermore,the energy efficiency(EE)of the HetNets under the proposed architecture is also evaluated,showing that the proposed user-selected uplink power control algorithm outperforms the traditional stochastic-scheduling strategy in terms of both capacity and EE in a two-tier HetNet.The other critical issues,including the tidal effect,the temporal failure owing to the instantaneously increased traffic,and the network wide load-balancing problem,etc.,are also anticipated to be addressed in the proposed architecture.(Abstract)

On Designing Consistent Extended Kalman Filter

This paper studies the consistency of the extended Kalman filter(EKF) for a kind of nonlinear systems. Based on the EKF algorithm, the authors propose the quasi-consistent EKF(QCEKF)as well as the tuning law for its parameters. The quasi-consistency of the proposed algorithm is proved.Finally, the feasibility of the algorithm is illustrated by the numerical simulation on an orbit determination example.

STRONG CONSISTENCY OF M ESTIMATOR IN LINEAR MODEL FOR NEGATIVELY ASSOCIATED SAMPLES

This paper discusses the strong consistency of M estimator of regression parameter in linear model for negatively associated samples. As a result, the author extends Theorem 1 and Theorem 2 of Shanchao YANG （2002） to the NA errors without necessarily imposing any extra condition.

Output Consensus for Heterogeneous Nonlinear Multi-Agent Systems Based on T-S Fuzzy Model

In this paper, the output consensus problem of general heterogeneous nonlinear multi-agent systems subject to different disturbances is considered. A kind of Takagi-Sukeno fuzzy modeling method is used to describe the nonlinear agents' dynamics. Based on the model, a distributed fuzzy observer and controller are designed based on parallel distributed compensation scheme and internal reference models such that the heterogeneous nonlinear multi-agent systems can achieve output consensus. Then a necessary and sufficient condition is presented for the output consensus problem. And it is shown that the consensus trajectory of the global fuzzy model is determined by the network topology and the initial states of the internal reference models. Finally, some simulations are given to illustrate and verify the effectiveness of the proposed scheme.

CONSENSUS CONTROL DESIGN FOR MULTI-AGENT SYSTEMS USING RELATIVE OUTPUT FEEDBACK

This paper studies the consensus problem of multi-agent systems in which all agents are modeled by a general linear system. The authors consider the case where only the relative output feedback between the neighboring agents can be measured. To solve the consensus problem, the authors first construct a static relative output feedback control under some mild constraints on the system model. Then the authors use an observer based approach to design a dynamic relative output feedback control. If the adjacent graph of the system is undirected and connected or directed with a spanning tree, with the proposed control laws, the consensus can be achieved. The authors note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.