非线性控制系统的拓扑结构

本文的目的是描述与分析非线性控制系统的拓扑结构.文中首先定义可线性化系统,然 后引入Whitney拓扑,并用此定义非线性控制系统族上的拓扑.在这个拓扑下,证明了除单 输入二维系统外,在一般情况下能线性化的系统是一个零测集.最后讨论一般反馈线性化问 题.对输入数仅比系统维数少一的情况给出了充要条件,并证明了在此情况下几乎所有的系 统均可线性化.     

k元n维冒泡排序网络的子网排除

在并行计算机系统中,元器件和线路故障普遍存在,而系统的容错能力可以通过其底层基础网络的拓扑性质衡量。为了精确度量以k元n维冒泡排序网络为底层拓扑结构的并行计算机系统的容错能力,结合其层次结构和子网划分特征,分别提出了节点故障模型和线路故障模型下攻击该网络中所有k－m元n－m维冒泡排序子网络的算法,确定了需要攻击的最优节点集合和最优线路集合。根据算法可得:当2≤k≤n－2,m≤k－1时,攻击k元n维冒泡排序网络中所有的k－m元n－m维冒泡排序子网络,在节点故障模型下需要攻击至少C^m_nm!个节点,在边故障模型下需要攻击至少C^m_nm!条线路。     

PI和PDI补偿器设计

本文研究了多变量线性时不变系统输出比例反馈—串联积分补偿器(简称PI补偿器)和输出动态反馈—串联积分补偿器(简称PDI补偿器)在闭路系统极点任意配置条件下的设计问题。文中通过矩阵[sI-A~r]~(-1)C~r的石既约分解导出了闭路系统特征方程的m×m多项式矩阵行列式表示式,据此建立了新的设计方法。对于PI和PDI补偿器证明了闭路系统极点可任意配置数分别为n≤min{2p+(m-1)[2p/m],n+m}和ηD≤min(v+vp+2p+(m-1)(2p/m],n+m+v}(n和v分别为系统和动态补偿器阶数,m为输出向量维数,p为控制向量维数,(2p/m)表示2p/m的整数部分,m≤p),并且该设计方法比已有的简单、实用。最后举例说明了它的应用。     

基于结点度和欧拉数的拓扑关系一般化描述

拓扑关系是GIS中空间目标间最基本、最重要的关系之一,然而目前的拓扑关系模型在描述两目标间的详细拓扑关系方面存在不足。针对二元目标间任意交的情况,提出了基于结点度和欧拉数的拓扑关系模型的一般化描述形式,使用目标整体间交(∩)、差(\\)两个集合算子的结果来区分目标间的拓扑关系,结果的取值包括内容、维数、结点度、欧拉数4个拓扑不变量。重点讨论了线/线、线/面和面/面拓扑关系一般化描述表达式。     

闭环控制系统的最经济结构综合问题

为任意配置线性定常闭环系统的n个极点,本文介绍了状态反馈阵或输出反馈阵的结构 特点,包括反馈阵必须含有的待定参数的最少个数及非零行(或列)、反馈变量的最少个数,并 介绍了为镇定一个不稳定系统,反馈阵必须具备的结构特点.最后给出了最经济反馈阵的设 计方法.     

离散广义系统的严格耗散分析与控制

对离散广义系统,考虑了关于二次型供给率严格耗散控制问题.建立了严格耗散与扩展严格正实之间的等价性.利用线性矩阵不等式(LMI),给出了离散广义系统严格耗散的充分必要条件,并着重推导了其成立的严格LMI条件.针对输入向量维数等丁状态向量维数的系统,分别利用非严格LMI及严格LMI,讨论了状态反馈下的严格耗散控制问题,并给出控制器的设计方法.也讨论了输入向量维数小于状态向量维数的情况.最后通过仿真算例说明所给方法的有效性和普遍性,同时显示了严格LMI条件在耗散控制问题中,比非严格LMI具有的优势.     

输出反馈极点配置的直接方法

本文研究了线性时不变能控能观系统x=Ax+Bu,y=Cx应用输出比例反馈和动态 补偿器任意配置闭路极点问题.文中借助于[sI-A]-1B矩阵的右既约分解矩阵,将闭路系统 特征多项式表示成p×p维矩阵行列式表示式,基于这一表示式建立了计算反馈矩阵和设计 动态补偿器的简单、实用的新方法.证明了应用输出比例反馈和动态补偿器可任意配置闭路 极点数分别为η≤min{max {m+(p-1) [m/p], p+(m-1) [p/m],n}和η0≤min {v+max {vm+m+(p-1)[m/p],vp+p+(m-1)[p/m]},n+v} (其中n和v分别为控制对 象和动态补偿器的阶数,p=rankB,m=rankC),文章最后举例说明了这种方法的应用.     

无限论域上粗糙集的拓扑结构

讨论了当论域不限制是有限集时满足自反、传递关系的广义近似空间中的近似算子的拓扑结构;证明了论域上满足自反、传递关系的集合与其上所有的拓扑的集合是一一对应的;指出了该拓扑空间的拓扑基.     

基于蜂窝结构的传感器网络覆盖问题求解算法

在无线传感器网络中,求解能够完全覆盖目标区域的最小覆盖集是个NP难问题.在传感器节点数目较多时,目前只能通过近似算法求解.蜂窝结构是覆盖二维平面的最佳拓扑结构,但不能直接用于求解无线传感器网络的覆盖问题.提出了一种基于蜂窝结构的覆盖问题求解算法,在该算法迭代求解过程的每一阶段,选出一个节点加入到初始为空的节点集合中,并使得该节点集合的拓扑结构接近于蜂窝结构,直至该节点集合成为覆盖集.该算法在最坏情况下的时间复杂度为O(n3),这里n为传感器节点总数.实验结果表明该算法可在很短的时间内执行完,在所得覆盖集的大小方面要优于现有的覆盖问题求解算法.     

一类交联大系统的分布控制: LM I 方法

以图的拓扑结构为基础，讨论由不同的交联子系统组成的大系统分布镇定控制器合成问题，首先通过例子描述了系统邻接矩阵的求法；然后给出了适定的概念；最后通过线性参变控制，获得了用有限维数线性矩阵不等式描述的充分条件。     

On Gnutella topology dynamics by studying leaf and ultra connection jointly in phase space

In this paper, the topology dynamics of Gnutella are studied in phase space. The dynamic progress of peer degree is studied as a time series in two dimensional phase space, which is consisted of numbers of connected leaves and ultras. The reported degrees concentrate on three special software related regions which we name as ultra stable region, leaf stable region and transition belt. A method is proposed on how to classify degree traces in phase space into different categories. Then the connection churn and the degree churn are studied. It shows that the topological structure of Gnutella is more stable in its connection degree than in the topology itself. The connection drop rate is estimated and the lifetime of connections is deduced afterwards. M/M/m/m loss queue system is introduced to model the degree keeping process in Gnutella. This model reveals that the degree stability is ensured by mass new connection efforts. In other words, the stability in topological structure of Gnutella is the results of many essential unstable factors in its topology. We think it raises a challenge to the basic design philosophy for such networks.     

运载火箭控制系统的BIT设计与实现

根据拓扑性质知觉原理,视觉原语是从整体到局部,拓扑感知优先。根据此仿生原理,建立感知目标物的形状拓扑信息的数学模型。首先提取物体三维轮廓信息;将空间图形轮廓降维映射到二维投影平面中进行处理;建立提取空间图形拓扑特征的数学模型。将轮廓拓扑空间同胚映射到(Hausdorf或度量空间或)二维投影平面,保持了拓扑不变性,因此便于分析出拓扑特征,可继续应用拓扑映射原理,分析点集拓扑。最终,拓扑特征与知识库模型相匹配,识别出物体。     

A global parametrization of asymptotically stable linear systems

In this paper we construct a homeomorphism from the set of p × m transfer functions of McMillan degree n onto the open subspace of asymptotically stable linear systems. This homeomorphism yields a one-to-one correspondence between

1. (i) canonical forms for state space equivalence of minimal systems and

2. (ii) canonical forms for state space equivalence of asymptotically stable minimal systems.

Implications for the topology of various sets of asymptotically stable systems are given.     

On intuitionistic fuzzy rough sets and their topological structures

In this paper, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of intuitionistic fuzzy approximation operators are examined. Relationships between intuitionistic fuzzy rough set approximations and intuitionistic fuzzy topologies are then discussed. It is proved that the set of all lower approximation sets based on an intuitionistic fuzzy reflexive and transitive approximation space forms an intuitionistic fuzzy topology; and conversely, for an intuitionistic fuzzy rough topological space, there exists an intuitionistic fuzzy reflexive and transitive approximation space such that the topology in the intuitionistic fuzzy rough topological space is just the set of all lower approximation sets in the intuitionistic fuzzy reflexive and transitive approximation space. That is to say, there exists an one-to-one correspondence between the set of all intuitionistic fuzzy reflexive and transitive approximation spaces and the set of all intuitionistic fuzzy rough topological spaces. Finally, intuitionistic fuzzy pseudo-closure operators in the framework of intuitionistic fuzzy rough approximations are investigated.     

非线性大系统在有限域中的鲁棒稳定性

本文研究了含有不确定参数的非线性大系统的稳定性,当参数向量受到限制时,这种稳定 性称为鲁棒(粗壮)稳定性.在状态空间的含原点的有限域中,利用李亚普诺夫函数进行集结 线性化,可将大系统化为线性系统,由于线性化的任意性,得到的线性系统不是唯一的.文 中阐明了利用图论方法建立的大系统的多层结构可以简化稳定性判据,帮助选择局部反馈,以 实现大系统的镇定.     

Design of minimal order stable observers for linear functions of the state via realization theory

Abstract--The design of a minimal order stable observer and a minimal order observer with arbitrary poles that estimates a vector linear function of the state of a multivariable system is discussed. It is shown that both problems can be solved in a straightforward manner using partial realization theory, and several new results are given. These include a strong bound for the dimension of the minimal order stable observer and a simple necessary condition to design the minimal order observer with arbitrary poles that estimates a vector linear function of the state of a multiple-output system. Necessary and sufficient conditions are given for designing a minimal order observer with arbitrary poles for the case of estimating a vector linear function of the state of a single-output system and the case of estimating a scalar linear function of the state of a multiple-output system. A procedure to carry out the design in each of these cases is described. No restrictions whatsoever (except stability) are placed on the possible values of the observer poles. A significant observation of this paper is that the dynamics of the observer are constrained (in all cases) only by the gain matrix in the feedback law to be estimated and the output structure of the given system.     

Stability analysis of the orbits of control systems

Extensive research in nonlinear system theory in recent years has shown that a number of system theoretic questions are closely related to the behaviour of the (controllability) orbits of the system. Thus orbit minimality, namely the property of the system having its state space identical to one orbit, arises naturally when dealing with controllability questions. This paper is concerned with the more general case where orbit minimality is not available, and attempts to explore various ways the orbits are patched together on the state space. Concepts like stability, attraction and asymptotic stability are defined and studied with the aid of certain sets naturally associated with the system like the limit set and the prolongational set. Since the related questions are topological in nature, the problems are set up using only the topological dynamics of the system.This work was supported in part by the National Science Foundation under Grants ENG 76-16812 and ENG 78-22166.     

Point-to-point regulation of a robot with flexible joints includingelectrical effects of actuator dynamics

This paper considers the set-point tracking problem in rigid and flexible-joint robots when both the mechanical as well as the electrical effects of the actuator dynamics are taken into account. The suggested controllers are based on state and output feedbacks. The current approach demonstrates that for every given desired operating point, linear state and output feedbacks with constant feedforwards can be constructed such that the closed-loop system is globally asymptotically stable     

Topological derivative-based topology optimization of structures subject to design-dependent hydrostatic pressure loading

In this paper the topological derivative concept is applied in the context of compliance topology optimization of structures subject to design-dependent hydrostatic pressure loading under volume constraint. The topological derivative represents the first term of the asymptotic expansion of a given shape functional with respect to the small parameter which measures the size of singular domain perturbations, such as holes, inclusions, source-terms and cracks. In particular, the topological asymptotic expansion of the total potential energy associated with plane stress or plane strain linear elasticity, taking into account the nucleation of a circular inclusion with non-homogeneous transmission condition on its boundary, is rigorously developed. Physically, there is a hydrostatic pressure acting on the interface of the topological perturbation, allowing to naturally deal with loading-dependent structural topology optimization. The obtained result is used in a topology optimization algorithm based on the associated topological derivative together with a level-set domain representation method. Finally, some numerical examples are presented, showing the influence of the hydrostatic pressure on the topology of the structure.