一组多输入非线性系统的同时镇定(英文)

考虑设计一个控制器同时镇定一组多输入非线性系统的问题.利用李雅普诺夫函数方法, 给出了时不变同时镇定状态反馈控制器存在地充分条件,然后给出构造同时镇定一组系统的连续控制器的统一公式. 该结果是对文献[1]中讨论的单输入系统的结论的推广.     

具有三阶中心流形的一类非线性系统的镇定

考虑了一类非线性系统的局部镇定问题.首先,利用正则型理论给出一类 3阶非线性系统稳定的充分条件;然后利用得到的结果以及中心流形理论,讨论一类具有特殊形式的 3阶中心流形的非线性系统的镇定问题,并给出中心流形的设计方法以及镇定系统的控制律.     

对一种模糊不完全权重求解模型的改进及其解法的探讨

文章对一种模糊不完全权重的求解模型进行简单阐述，指出其不足，对该求解模型进行更符合实际意义的改进，同时提出一种更加简便的该模型的求解方法。     

求解线性规划的单纯形法探讨

线性规划的单纯形法是求解线性规划问题的一种方法,同时在运筹学教学中这也是一个难点。笔者参照了大量文献,分析了单纯形方法教学的难点问题,通过实例论证如何用单纯形矩阵法求解线性规划问题。同传统的教学课本而言,如果用此方法去求解线性规划问题不仅优化了教学流程,也减少了学生学习的难度。     

自由意志与当代实验哲学：回顾、反思与展望

自由意志问题作为一个经典的哲学论题至今仍引发着不断的争论。当代哲学关于其讨论主要集中于相容论与不相容论之争。实验哲学作为一种新的哲学方法,挑战了一些传统哲学家的论断,同时探究了人们关于自由意志问题直觉下的心理机制,揭示出情感、人格特征以及对决定论场景的描述都会影响人们关于相容论问题的判断。但当前实验哲学的工作对决定论情境的描述存在着一些困难,并且也并未研究不相容论者所诉诸的具体原则或论证前提的直觉。然而,对这些困难和不足的反思也正提供了未来对自由意志问题研究的积极启示。     

级数问题中几种值得注意的求解方法

该文给出了三类级数问题的求解思路,通过实例说明级数问题中三种值得注意的方法,同时展现出级数问题求解的一些技巧.     

具有时变不确定参数的线性时滞系统的鲁棒镇定

研究了具有时变不确定参数的线性时滞系统的鲁棒镇定问题．提出鲁棒稳定化控制器一种新的设计方法．现有的一些结果可以作为本文的一些特例得到．     

蚁群算法在LQ最优控制逆问题中的应用

蚁群算法是一种模拟进化算法，初步的研究表明该算法具有许多优良的性质．研究了一种可用于求解连续空间优化问题的蚁群算法策略，针对SISO离散时不变控制系统，在给出了加权矩阵Q与状态反馈阵K的取值范围确定方法的基础上，应用连续性空间优化问题的蚁群算法模型求解了离散LQ逆问题。仿真结果表明蚁群算法在求解控制优化问题中的有效性。     

颜氏水火相容热水炉获准进京

颜氏水火相容热水炉获准进京水同火，无人不晓这是一对冤家。熊熊烈火．一场倾盆大雨即可瞬间扑灭。因此．水火不相容，几乎成了千古训律。湖南长沙发明家颜孟秋发明的水火相容（直接）换热炉，恰恰是取消了换热传热面（锅、管等），使水同火相混相容．破千古常规．立全新...     

随机非线性系统的控制器设计和闭环性能分析

针对几类重要的随机非线性系统, 提出了一些新的概念,发展了一些基本分析工具, 研究了几类控制器的设计问题. 主要成果包括:(1) 针对一类部分动态不可量测的非线性随机系统,引入了随机输入状态稳定(SISS)的概念, 借助于分析概率理论,发展了随机系统改变能量函数方法, 成功地处理了随机微分中的伊藤项,给出了随机非线性串联系统SISS的小增益类条件. (2) 对一类具有SISS随机逆动态的大规模随机非线性系统,给出了分散自适应输出反馈镇定控制器的构造性设计方法. 既解决了实用镇定问题也解决了渐近镇定问题. 在分散控制框架内,给出了处理随机非线性逆动 态的方法. (3) 对一类具有不稳定零动态的随机非线性系统,引入了随机输入状态可镇定的概念,给出了全局输出反馈镇定控制器构造性设计方法. (4) 对一类具有线性增长的不可量测状态的随机非线性系统,针对方差未知的噪声和一般随机输入,引入了广义随机输入状态稳定(GSISS)的概念,分别给出了随机干扰抑制和渐近镇定的输出反馈控制器的构造性设计方法.(5) 对一般的时滞随机非线性系统, 给出了解存在唯一的判定条件,引入了依概率全局(渐近)稳定的概念及相应的判定准则,丰富了随机时滞非线性系统的控制器设计理论. 对一类不确定随机时变时滞系统,构造性地设计出了自适应输出反馈镇定控制器.     

Optimal parametrization in numerical construction of curve

The application of the optimal parametric continuation method to constructing a solution set curve for a system of nonlinear algebraic or transcendental equations depending on a parameter is considered. There are discussed two approaches to solving this problem—the use of iterative methods and reduction to an initial value problem for a system of ordinary differential equations. The algorithm suggested in this paper can also be used for finding an appropriate initial approximation when solving a system of nonlinear algebraic or transcendental equations not depending on a parameter by an iterative method.     

Dyadic analysis of space rigid framework

Any space framework consisting of prismatic beams and rigid joints may be analyzed exactly by solving a set of simultaneous linear vector equations with dyadic coefficients. The iteration method may be applied equally well.     

On a Method of Solving Sensitive Boundary Value Problems

Nonlinear two-point boundary value problems have always been difficult to solve. The difficulty is compounded if the problem tends to be inherently unstable. This paper describes an algorithm for solving such sensitive boundary value problems. The procedure is based on a computational method for finding the general solution of systems of ordinary differential equations used in conjunction with the multi-point quasilinearization method of Miele. The method is demonstrated by solving Troesch's problem and a singular perturbation problem.     

An adaptive mesh method with variable relaxation time

Moving mesh partial differential equations have been widely used in the last decade for solving differential equations exhibiting large solution variations such as shock waves and boundary layers.In this paper, we have applied a dynamic adaptive method for solving time-dependent differential equations. The mesh velocities are governed by an equation in which a relaxation time is employed to move nodes in such a way that they remain concentrated in regions of rapid variation of the solution. A numerical example involving a blow-up problem shows the advantage of using a variable relaxation time over a fixed one.     

State feedback uniform decoupling problem of linear time-varying analytic systems

A new approach to the input-output uniform decoupling problem of linear time-varying analytic systems via proportional state feedback is presented. A major feature of the proposed approach is that it reduces the solution of the uniform decoupling problem to that of solving a linear algebraic system of equations. This system of equations greatly facilitates the solution of the three major aspects of the decoupling problem: the necessary and sufficient conditions, the general analytical expressions for the controller matrices, and the structure of the uniformly decoupled closed-loop system.     

一种基于laplace变换求解跳变问题的新方法

信号与系统课程是电子信息类专业的核心基础课程,在各种经典教材中都采用冲激响应匹配法求解微分方程零时刻的跳变值。本文分析了冲激响应匹配法求解跳变问题存在的问题,提出了一种应用laplace变换求解跳变问题的新方法,简述了此种方法的原理和求解过程。多年的教学经验表明这种方法更简单,更易让学生掌握。     

利用二次函数思路巧解不等式问题

在学习中,我们常常会遇到解方程及不等式问题,按常规方法很难分析得出结果,但是利用二次函数思想经过分析,问题就可以迎刃而解了。     

Mathematical aspects of static and dynamic stability problems in power systems

A power system is modelled by a system of parameterised differential-algebraic equations (DAEs) when it is operating normally; it is modelled by time-piecewise DAEs when a transient process occurs. The normal operation of power systems is related to the static stability problem; while the transient process is related to the dynamic stability problem. After categorising the stability problems in power systems into static and dynamic cases, mathematical formulations are proposed and mathematical problems related to them are studied using different mathematical tools. In the static case, the determination of feasibility region is related to solving algebraic equations; while in the dynamic case, identifying attraction domain is related to solving a DAE. For a power system, the determination of feasibility region is usually reduced to optimisation problems, while the determination of attraction domain and critical clearing time is related to the study of transient energy functions.     

Exact Model-Matching of 2-D Systems via State Feedback

This paper considers the problem of matching the transfer function matrix of a given two-dimensional (2-D) system to that of a desired 2-D model using state feedback. The approach followed refers to systems having square transfer function matrices and reduces the problem to that of solving a linear system of equations. Furthermore, necessary and sufficient conditions are established for exact matching. An example is included to illustrate the proposed method.     

非吸收椭球形粒子尺度分布反演的一种新方法

研究了非吸收椭球形粒子尺度分布的反演问题.对于连续消光谱,得到了尺度分布与消光系数之间一个新的变换关系.对于离散消光谱,给出了基于Gamma分布展开的粒子尺度分布函数的级数表示,其中展开系数可通过求解相应的约束线性方程组来确定.在某种给定的反演精度下,实施积分所需的最短应测量波长与最小可反演粒径成正比.数值试验表明,本文所发展的解析技术是有效的,可容忍消光谱约5%的随机误差.