一类混杂动态系统的能控性(Ⅲ)--含多时滞的情形

首次将时滞现象引入到线性切换系统的模型中，研究含有时滞线性切换系统的能控性及其判定条件．全部工作由三部分组成．第Ⅲ部分，主要研究含多时滞的线性切换系统的能控性及其判定规则．首先给出周期型系统的单周能控性和多周期能控性的定义和充要条件，其次给出非周期系统的能控性的定义和充要条件．最后，研究时滞大小不一致的情形，指出能控性与时滞大小无关．     

一类混杂动态系统的能控性（I）——基本结果

首次将时滞现象引入到线性切换系统的模型中，研究含有时滞线性切换系统的能控性及其判定条件．全部工作由三部分组成，第I部分首先，提出含时滞的线性切换系统的数学模型，并介绍切换系统的基本概念——切换序列．其次，引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念，给出一些有关概念的基本性质，特别是分离引理．然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系，这个引理将在能控性的判定中起关键作用．这些概念和引理都将作为以后展开能控性分析所必需的研究工具．     

用优化方法解接触问题—试算谐波减速器中的柔轮应力

直接应用通常的有限单元程序来解接触问题会遇到数值困难.本文用极值形式表达接触问题,并用优化方法求解.它并不要求事先给出所有边界条件,而只要给出约束条件就可以了,因而特别适宜于求解接触问题.用本文提出的方法对上海交大制造的谐波减速器中的柔轮应力进行了试算,结果与实验数据基本相符.     

直流脉冲电压式静态应变测量

本文提出了对电阻应变片采用脉冲加电来测量静态应变的方案。和一般的电阻应变仪相比,它具有信噪比高、环境热干扰影响小、测量快速等优点。在测量桥路输出处加接了一个高共模抑制的运算放大器,使普通数字电压表可以用来实现A/D转换,简易地实现了数字化。     

COMPUTING THE EIGENVECTORS OF A MATRIX WITH MULTIPLEX EIGENVALUES BY SVD METHOD

Every matrix is similar to a matrix in Jordan canonical form, which has very important sense in the theory of linear algebra and its engineering application. For a matrix with multiplex eigenvalues , an algorithm based on the singular value decomposition ( SVD ) for computing its eigenvectors and Jordan canonical form was proposed. Numerical simulation shows that this algorithm has good effect in computing the eigenvectors and its Jordan canonical form of a matrix with multiplex eigenvalues. It is superior to MATLAB and MATHEMAtICA.     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME_DELAY CASE

IntroductionConsideraswitchedlinearsystemwithsingletime_delayinthecontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) +Dr(t) u(t -τ) ,(1)wherex(t) ∈Rnisthestate,u(t) ∈R mtheinput,thepiecewiseconstantscalarfunctionr(t) :R+ → 1,2 ,… ,Nistheswitchingpath ,(Ai,Bi,Di) ｜i =1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimpliesthat(Ai,Bi,Di)ischosenasthesystemrealizationattimet.τ >0isthefixedtimedelayincontrol.Inthispaper ,wewillstudythecontrollabilityofsystem (1) .Theone_per…     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME_DELAY CASE

IntroductionConsidertheswitchedlinearsystemwithmultipletime_delaysincontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) + Kk=1Dr(t) ,ku(t -τk) ,(1)wherex(t) ,u(t)andr(t)isdefinedasbefore ,(Ai,Bi,Di,1,… ,Di,K)｜i=1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimplies (Ai,Bi,Di,1,… ,Di,K)ischosenasthesystemrealizationattimet.K <∞isthenumberoftime_delaysinthesystem .0<τ1<… <τKareKfixedtime_delays .Remark 1　Similarly ,wecandescribeswitchingpathbyintroducingswitchingsequ…     

SOLVE A CONTACT PROBLEM BY OPTIMIZATION METHOD—TO CALCULATE THE STRESSES FOR THE SOFTWHEEL IN A HARMONIC GEAR

It is difficult to solve the contact problem by usual finite element program. In this paper, we express the contact problem as an optimization problem. In this form we do not need to know all boundary condition in advance. We only need to know the constraint conditions. This method is especially good for solving contact problem. Using this method, we calculate the stresses of the softwheel in the harmonic gear given by Shanghai Jiaotong University, and the results are in good agreement with the experimental results.     

一类混杂动态系统的能控性(Ⅰ)--基本结果

首次将时滞现象引入到线性切换系统的模型中,研究含有时滞线性切换系统的能控性及其判定条件.全部工作由三部分组成,第Ⅰ部分首先,提出含时滞的线性切换系统的数学模型,并介绍切换系统的基本概念--切换序列.其次,引入列空间、循环不变子空间和广义循环不变子空间等基本几何概念,给出一些有关概念的基本性质,特别是分离引理.然后以一个基本引理的形式揭式某一积分方程的解集与广义循环不变子空间之间的联系,这个引理将在能控性的判定中起关键作用.这些概念和引理都将作为以后展开能控性分析所必需的研究工具.     

SOLVING LYAPUNOV MATRIX EQUATION A~TP+PA=-Q BY OPTIMIZATION

This paper discusses a new method for soving matrix Lyapunov equation. It is a quite efficient method. It needs about 6(5/8)n~3 multiplications for solving a Lyapunov equation of order n. Two numerical examples are given.