Global Topological Linearization with Unbounded Nonlinear Term

In 1960s, Hartman and Grobman pointed out that if all eigenvalues of a matrix A have no zero real part and f(x) is small Lipchitzian, then x′=Ax+f(x) can be locally linearized on a neighborhood of the origin. Later, the above result was generalized to global under the condition that f(x) is a bounded function. In this paper, we delete the condition that f(x) is a bounded function, and prove that if f(x) has suitable structure, then x′=Ax+f(x) can be linearized.

Group-Consensus of Hierarchical Containment Control for Linear Multi-Agent Systems

The existing containment control has been widely developed for several years, but ignores the case for large-scale cooperation. The strong coupling of large-scale networks will increase the costs of system detection and maintenance. Therefore, this paper is concerned with an extensional containment control issue, hierarchical containment control. It aims to enable a multitude of followers achieving a novel cooperation in the convex hull shaped by multiple leaders. Firstly, by constructing the three-layer topology, large-scale networks are decoupled. Then,under the condition of directed spanning group-tree, a class of dynamic hierarchical containment control protocol is designed such that the novel group-consensus behavior in the convex hull can be realized. Moreover, the definitions of coupling strength coefficients and the group-consensus parameter in the proposed dynamic hierarchical control protocol enhance the adjustability of systems. Compared with the existing containment control strategy, the proposed hierarchical containment control strategy improves dynamic control performance. Finally, numerical simulations are presented to demonstrate the effectiveness of the proposed hierarchical control protocol.

ON CONDITIONS FOR THE NON LOCALLY CONVEX LINEAR TOPOLOGICAL SPACE TO HAVE THE H．－B． EXTENSION PROPERTY

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基于加权最小绝对值状态估计的有源配电网拓扑辨识方法

在配电系统状态估计中,一方面众多网络设备难以完全监控导致量测数据不足,另一方面,频繁的拓扑切换亟须开发高效的算法。因此,提出了一种配电网拓扑辨识的加权最小绝对值状态估计方法。首先,对传统基于线性规划的加权最小绝对值状态估计方法进行改进,以提高计算效率;其次,在重新制定的加权最小绝对值状态估计方法中加入补充变量和约束,以适应拓扑辨识问题,形成了一个基于混合整数线性规划的加权最小绝对值状态估计方法;最后,4个算例系统的仿真结果验证了所提方法在不同数量的实时测量、高伪测量误差、被坏数据破坏的测量以及未知支路状态场景下的优异性能。

双层蜂窝状海森伯铁磁体中层间交换耦合相互作用对拓扑相的影响

层状磁性拓扑材料是最小二维单元下同时具有磁序和拓扑性的材料体系,研究这一体系可能会观察到新物性和新现象的出现,因此引起了研究者们的广泛关注.本文运用线性自旋波理论,主要研究了层间铁磁耦合的双层蜂窝状海森伯铁磁体中层间交换耦合相互作用对系统拓扑相的影响.通过计算不同层间交换耦合相互作用强度下的磁子色散关系能得出,当系统达到两个强度临界值时,能量较高的两条能带和能量较低的两条能带的带隙在狄拉克点处会依次出现闭合-重新打开现象.计算能带对应的贝里曲率和陈数后,发现贝里曲率符号在相应临界值前后会发生反转,同时陈数也会发生改变,这证明系统发生了拓扑相变.此外,本文研究发现当双层蜂窝状铁磁体发生拓扑相变时,磁子热霍尔系数变化曲线会相应发生突变.本研究成果可以为利用双层蜂窝状铁磁材料制作具有更高信息传输能力的自旋电子器件提供理论支撑,也可以为其他双层铁磁系统的相关研究提供一定的理论参考.

基于希尔伯特变换的电网络约束关系研究

为了研究电压波动条件下的电网络约束关系,文章基于希尔伯特变换,构建了供电电压存在波动下线性时不变负载上电压、电流的解析信号模型,推导出了以解析信号表征线性时不变电网络的拓扑约束和元件约束关系,将相量法思想拓展至对供电电压波动下线性时不变电网络响应特性的分析与求解。仿真验证结果表明,供电电压存在波动条件下,文中所建立的基于希尔伯特变换的电网络约束关系,不仅物理意义清晰、表征简明,而且正确、好用。文章所建立的电网络约束关系,能够为供电电压波动条件下电网络中线性时不变负载上电压电流关系的建模、仿真分析与计算提供指导。

针对负荷重分配攻击的移动目标防御策略

负荷重分配攻击考虑电力系统实际设备配置及实际运行情况,通过篡改负荷量测对电力系统安全稳定运行造成威胁。提出一种基于拓扑变换的移动目标防御方法,通过变换系统拓扑结构破坏攻击者对电力系统信息的掌握程度,实现对负荷重分配攻击的防御,为电力系统安全可靠运行提供保障。首先,建立负荷重分配双层优化模型,对攻击策略进行分析;然后,分析拓扑结构的优化重构方式,建立拓扑结构变换的优化模型;最后,将拓扑结构优化算法与状态估计相结合实现移动目标防御,完成对负荷重分配攻击的检测。在IEEE 14节点系统中对所提方法进行了测试与分析,算例证明基于拓扑变换的移动目标防御方法能够对负荷重分配攻击进行有效防御,增强电力系统的抗攻击能力。

拓扑优化结构中棋盘格式的光滑及等面积处理方法

为了解决拓扑优化后出现的边缘棋盘格式问题,提出了用线性最小二乘法对边缘棋盘格式进行线性化处理。在拓扑优化棋盘格式边界线性化处理后,出现了小梁结构端面面积在长度方向不相等和不均匀等问题,对实际工程应用带来不便。针对此问题提出了首先用常规的单边中心分割等面积处理方法对线性光滑处理后的模型进行优化,使重构模型趋于均匀化、规则化,但是发现单边中心分割等面积法处理后重构模型的小梁中心出现了偏离。为了保证小梁结构端面面积相等、同时保证小梁中心线不偏离,又提出了双边中心分割等面积法,这种方法避免了小梁结构等面积变化后的中心线偏离问题,保证拓扑优化结构的完整性。通过计算对比分析,发现双边中心分割等面积法处理后的重构模型在静力学分析中的性能均优于其他两种方法,验证了双边中心分割等面积法处理的可行性。

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Space Topologies and Their Dual Space Topologies for Conventional Functional Space Topologies

In this paper, we have studied the topology of some classical functional spaces. Among these spaces, there are standard spaces, spaces that can be metrizable and others that cannot be metrizable. But they are all topological vector spaces and it is in this context that we have chosen to present this work. We are interested in the topology of its spaces and in the topologies of their dual spaces. The first part, we presented the fundamental topological properties of topological vector spaces. The second part, we studied Frechet spaces and particularly the space S(Rn) of functions of class C∞ on Rn which are as well as all their rapidly decreasing partial derivatives. We have also studied its dual S'(Rn) the space of tempered distributions. The last part aims to define a topological structure on an increasing union of Frechet spaces called inductive limit of Frechet spaces. We study in particular the space D(Ω) of functions of class C∞ with compact supports on Ω as well as its dual D' (Ω) the space distributions over the open set Ω.

一类分段线性连续动力系统的边界混沌分岔

研究了一类三维分段线性连续系统从稳定平衡点突变到混沌不变集的边界平衡点分岔现象。首先,验证了同宿轨和异宿轨的不存在性,从而说明系统的混沌现象是非Shil'nikov混沌。进一步,通过在切换面上寻找合适的Poincaré截面,并通过两个子系统混合流作用建立二次返回Poincaré截面映射,再利用拓扑马蹄理论,给出系统混沌不变集存在性的计算机辅助证明。

基于多源数据融合的配电网拓扑识别方法研究

针对目前配电网拓扑识别时多源融合数据利用率低的问题,提出了一种基于多源数据融合的配电网拓扑识别方法。首先,设计了一种多源数据时间尺度对齐方法。其次,提出了一种基于线性外推的伪测量数据生成方法,从而提高拓扑识别方法的数据精度。最后,建立了多源数据融合配电网离散化和线性化最优拓扑识别方法。在试验阶段,以IEEE 33馈线系统为例验证所提方法。试验结果表明,当节点注入功率数据的实时测量误差为30%、伪测量误差为5%时,所提方法拓扑识别准确率为70.98%,较无融合方法提升了5.86%。所提方法对提高配电网拓扑识别准确率具有一定指导作用。

基于迭代隐式线性化的网状配电网潮流计算及其最优潮流模型

随着分布式能源和储能容量的增加以及电动汽车的普及,配电网的功率流动由单向转变为双向,且网络拓扑由径向转变为复杂的网状结构。为了高效应对网状配电网的潮流(power flow,PF)分析和最优潮流(optimal power flow,OPF)问题,以及进一步提升现有线性化模型的近似精度、完善对网络损耗等元素的线性近似,该文构建迭代隐式线性化潮流(iterative implicit linearization power flow,IIL-PF)模型及其最优潮流模型(IIL-OPF)。该模型将非线性潮流流形M(Manifold)视为节点电压和节点注入功率之间的隐式代数关系,之后利用切平面对M进行局部近似,并迭代更新线性化点以提高线性模型的近似精度。此外,所提模型充分考虑了支路始/末端潮流、支路潮流平方、支路损耗等因素,并对其进行明确的线性化推导。最后,基于修改的IEEE 33系统,分别在径向和网状运行方式下,验证所提模型可快速收敛,并具有较高的近似精度。其中IIL-PF计算结果、IIL-OPF的目标函数和发电机出力等优化结果与MATPOWER的非线性模型相比,误差均在1%以内,因此所提模型可以满足工程规划或日前运行模拟等应用要求。

Inductive Topologies of L-fuzzy Topological Vector Spaces

In this paper, using the theory of L _fuzzy topological vector spaces [1]-[6] , we study some properties of L _fuzzy inductive topologies determined by a family of L _fuzzy linerar order_homomorphisms [2] of L _ftvs, and give a characterization of inductive topologies determined by a single FLOH. As an application of this results, we prove that the quotient space of L _ftvs is also L _ftvs.

ARCGIS软件在第三次国土调查中应用研究

ARCGIS软件是测绘地理信息项目中常用软件。第三次国土调查是作为一项在国情国力方面的调查,其目的是调查清楚全国土地资源利用情况和国土地类现状,为以后诸如国土空间规划、基本农田划定、生态文明建设等方面提供基础数据和政策导向。在第三次国土调查中,ARCGIS为内业数据处理提供了强大的技术支撑。ARCGIS软件可对线状地物图斑化和野外举证数据提前批处理进行详细的研究,在水利、农业、生态、交通、林业、住建等方面都有非常广泛的应用。

大模型辅助的大型海上风电场集电系统拓扑优化

集电系统拓扑优化是大型海上风电场规划建设的核心问题,本质上是一个涉及多约束、多目标的复杂混合整数优化问题。针对该问题,提出了一种基于大语言模型(large language model,LLM)辅助的大型海上风电场集电系统拓扑优化方法。首先,基于大语言模型辅助对风电机组群进行聚类,通过链式提示法使LLM理解优化目标,并利用LLM将大型海上风电场分割为若干小型区域,以降低优化问题维度,提升求解速度和质量。然后,构建集电系统拓扑优化模型,基于混合整数线性规划求解器,获得海上风电场的最优集电系统拓扑设计方案。最后,利用1个含有75台风电机组的大型海上风电场系统进行方法性能验证,仿真结果表明:与传统优化技术相比,所提方法获得的聚类风机数量更加均衡,在考虑拓扑功率损耗的同时,生成的拓扑方案经济性最优。LLM在集电系统拓扑辅助优化中具有较高的有效性,为海上风电场集电系统拓扑设计优化提供了一种新思路。

A Synchronous and Deterministic MAC Protocol for Wireless Communications on Linear Topologies

Linear topology is useful in several pervasive application scenarios. Even though a linear topology can be handled by unspecific routing algorithms over general purpose MAC protocols, better performance can be obtained by specialized techniques. This paper describes a new communication scheme called Wireless Wire (WiWi), which builds up a bidirectional wireless communication channel with deterministic properties in terms of throughput and latency over a strip of pervasive devices with short-range transmission capabilities. The system is synchronous and fault tolerant. With low cost and extremely simple devices, WiWi builds up a “wire-like” dielectric link, but its applications are not limited to end-to-end communications. For example, WiWi can be used to collect data from sensors along the path, thus acting as a virtual conveyor belt.

Spatial Topology Rule Checking Algorithm of Linear Entity Based on Quadtree

Spatial topology rule is the primary method to insure the consistency and validity of spatial topology relation in GIS software. Topology rule can be divided into three categories according to geographic entity’s geometric shape: point topology rule, line topology rule and polygon topology rule. At first, this paper summarizes the various linear geographic entities’ topological relations which have practical application, then designs a series of linear entity topology rules detailedly. Based on these rules, this paper proposes a topology rule checking algorithm using quadtree, which is designed on the basis of MAPGIS7.4 spatial data model. The algorithm has already been applied to MAPGIS platform and gained good effects.

Recent Development of Linear Machine Topologies and Applications

Linear machines(LMs)produce linear motion without any intermediate transmission mechanisms,thus the whole electromechanical system has simple structure and its efficiency is high.Because of such merits,linear machines have been studied for a long time and rapidly developed in recent years.Due to the characteristic of open structure,linear machines have more diversity than rotary machines in terms of machine topologies.Accounting for the wide applications of linear machines,e.g.Maglev train,precision machine tools,semiconductor processing device,automatic equipment,logistic transport line,ropeless lifter,compressor,etc.,this paper reviews the most applied linear machines including machine topologies,operating principle and features.In addition,the influence of end effects and the corresponding reduction methods are also summarized.Finally,several commercial applications are exemplified.