多变量定常线性系统的传输零点与结构无静差性质

文献[1—4]详细研究了多变量定常线性系统的无静差和结构无静差性质,得到了内模原理的频域形式.为了说明内模原理的实质,本文讨论了无静差和结构无静差系统的传输零点的作用.本文所得结果告诉我们,多变量定常线性系统的无静差或结构无静差性质,是由闭环系统的零点与外部输入信号的极点之间的零极相消来保证的.本文使用与参考文献[1,2]相同的符号与术语.我们先对“结构稳定”的概念给一个确切的定义.如果一个多变量定常线性系统具有某种性质 π,并且在该系统的某个标称参数点 P 处存在某个邻域 U,使得这个系统在邻域     

控制系统结构稳定性的一种定量分析方法

§1.引言及问题文[1]应用矩阵扰动分析方法研究了线性控制系统的结构稳定性,得到了闭环系统关于矩阵范数‖·‖2(?)‖·‖_F 和 ‖·‖_∞在标称参数点 P_0处的结构稳定裕度下界的一系列估计公式。受扰闭环系统保持无静差只是一个基本的要求,受扰闭环系统的其它动态品质指标的变化也是应考虑的。由于系统的谱的分布对其动态品质有很大的影响,为此需要研究使受扰闭环系统不仪保持无静差,且使其谱的分布在一个预先指定范围内变化的结构稳定问题。     

关联系统可靠镇定的开关分层控制法

本文建立了一种具有开关的双层控制方案,其中每一层均采用分散控制结构.并且只有第二层带有开关参数.进而说明,对一个由两个线性时不变子系统任意线性关联构成的大系统,存在所述的分层控制器使得导致的闭环系统,在任意关联结构扰动下都保持稳定的充分必要条件,是原正常关联的大系统作为具有双通道的分散系统,没有不稳定的固定模并且每个子系统均是能稳、能检测的.     

具有输入时滞的汽车主动悬架系统的鲁棒指数镇定

针对具有输入时滞及控制量和输出约束的汽车主动悬架不确定系统,研究了鲁棒H_∞指数镇定问题.通过设计状态反馈控制器,使得闭环系统鲁棒指数稳定,并且能够有效地抑制外界干扰.通过实例仿真验证了所设计控制器的有效性和可行性.     

奇异脉冲系统的奇异H_∞控制

主要研究奇异脉冲系统的奇异H∞控制问题.当系统不满足正则条件时,给出奇异脉冲系统的奇异H∞控制问题可解的充分条件,控制律使得闭环系统在保证内稳定的条件下达到干扰衰减.     

PMSM系统的参数稳定性分析和自适应控制

针对含未知参数的永磁同步电机(PMSM)系统,研究其参数稳定性和自适应控制问题.首先,分析了参数变化对PMSM系统平衡点的影响.然后,通过设计自适应控制器使得闭环系统具有耗散Hamiltonian结构,使闭环系统的能量分布随着未知参数的漂移而自动的改变,且能量函数总在未知参数对应的平衡点处取得极小值,从而实现自适应参数...     

基于增益调度解耦控制的飞行控制系统研究

针对一类非线性系统,设计了增益调度解耦控制律,且给出了定量的闭环特性分析.在控制系统分析中,建立了闭环系统阶跃响应和动态性能指标关于控制参数的数学表达式,从而克服了许多控制算法中参数试凑的盲目性和重复性.此外,在控制律实现中,为保证作为调度变量的系统输出缓慢变化,且为避免工作点处实际模型和线性模型之间的大偏差以及控制量的瞬时值过大或是振荡,提出进行参考信号变换,即阶跃跳变部分都用正弦信号去替代.为验证所设计控制律的可行性和有效性,将其应用于四旋翼飞行器的飞行控制中.根据四旋翼飞行器的结构特性和运动原理,设计了递阶形式的飞行控制结构,并采用所提出的增益调度解耦控制律分别设计外环的位置控制器和内环的姿态控制器.飞行仿真结果表明所设计的飞行控制系统结构和所提出的控制律具有可行性和有效性.     

两端固定n根系列连接的Timoshenko梁在连接点加控制的镇定问题

文章研究两端固定n根系列连接的Timoshen]K0梁系统的镇定问题,假设该系统在连接点处剪切力和弯曲力矩是连续的,而横向位移和旋转角度是不连续的.在连接点处设置控制器,观测节点处的力,通过补偿器补偿后反馈回系统,构成闭环系统.通过对系统的矩阵化处理,对算子谱采用渐近分析的技巧,证明得到该闭环系统是渐近稳定的.并利用算子谱的分布等性质,在一定条件下得到了闭环系统的Riesz基性质,从而系统满足谱确定增长条件.     

具有分布反馈和边界反馈的非均质Timoshenko梁的指数镇定性

讨论具有分布反馈控制和边界反馈控制的非均质Timoshenko梁的指数镇定问题.首先利用已有的关于线性分布参数系统的渐进稳定性判据,证明所论梁系统的能量可仅由一个分布反馈控制指数镇定.进而利用频域分片乘子方法,在所论梁系统同时具有分布反馈控制和边界反馈控制的条件下,证明其相应的闭环系统能量指数稳定.     

一类动态系统可靠 D -稳定性条件 - LMI方法

考虑一类具有执行器和传感器故障的动力系统可靠鲁棒控制综合问题. 提出了一个系统 D -稳定的充分必要条件. 基于这一充分必要条件, 得到了可靠 H_∞ 控制器存在的条件. 接着用线性矩阵不等式(LMI)方法设计控制器, 使闭环系统当部分控制器件出现故障时鲁棒 D -稳定且具有H_∞性能. 最后通过一个仿真实例说明该文给出的方法及其有效性     

Various motivations for managerial (mis)reporting – an experimental study

In the experiment we model all possible consequences from misreporting for both the shareholder and for the manager, since we are interested in patterns in reporting behaviour resulting from different motivations for potential misrepresentation. This allows for examining the stability of the (mis)reporting behaviour in different treatments. Agents are primarily driven by the consequences for themselves rather than by the consequences for the principal, while deciding on misreporting. Participants are willing to sacrifice a small gain for themselves in order to prevent a greater loss for the principal. If agents misreport, they do it in order to generate positive rather than negative consequences for themselves. Reports in favour of the principal, but fruitless or even costly for the agent are very rare. The experiment indicates also that pro-social agents report more truthfully than pro-self agents.     

City-effects in the atomic bomb survivors data

It was investigated how risk estimates derived from the RERF life span study data sets for cancer incidence and mortality, respectively, differ between the two cities Hiroshima and Nagasaki, and the two sexes. This was done by estimating the excess risk for various age-at-exposure and time-since-exposure groups. The epidemiologically most reliable age group are those aged 20–39 years at the time of exposure. As expected, in this group, the relative risk for females in Hiroshima is higher than that for males; however, in Nagasaki, the relative risk for females is lower than that for males. When comparing the risks in the two cities for the same sex, the risks of cancer incidence and mortality of females exposed in Hiroshima are higher than those in Nagasaki. However, for the males, the risks of cancer incidence in Hiroshima are lower than in Nagasaki, and the risks of cancer mortality of males are very similar between both cities. All differences depend on age-at-exposure and time-since-exposure, and are at the borderline of being statistically significant. The absorbed dose of neutrons, for the same γ-dose, is about three times as high in Hiroshima than in Nagasaki for both sexes. Because of these observed risk differences between both cities, it does not appear to be possible to reliably estimate the relative biological effectiveness of neutrons as compared to that of γ-rays from these epidemiological data sets. No evidence was found in this analysis that the radiation weighting factors w_R presently used for neutrons in radiation protection could severely underestimate the risks for somatic late effects induced by neutrons.     

流动稳定性弱非线性理论的重新考虑*

弱非性理论已被广泛用于流动稳定性理论及其它领域.然而其应用对某些问题虽是成功的,但对另一些问题,其结果却常不令人满意,特别是对转捩或自由剪切流中涡的演化这类问题,这时理论研究的目的不是寻找稳态解,而是预测演化过程.在本文中,我们将研究不成功的原因并建议一些改进的办法.     

Bounds for Shannon and Zipf‐Mandelbrot entropies

Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy.     

Half Space and Quarter Space Dirichlet Problems for the Partial Differential Equation

A customary, heuristic, method, by which the Poisson integral formula for the Dirichlet problem, for the half space, for Laplace's equation is obtained, involves Green's function, and Kelvin's method of images. Although this heuristic method leads one to guess the correct result, this Poisson formula still has to be verified directly, independently of the method by which it was arrived at, in order to be absolutely certain that a solution of the Dirichlet problem for the half space, for Laplace's equation, has been actually obtained. A similar heuristic method, as seems to be generally known, could be followed in solving the Dirichlet problem, for the half space, for the equation where is a real constant. However, in Part 1, a different, labor-saving, method is used to study Dirichlet problems for the equation. This method is essentially based on what Hadamard called the method of descent. Indeed, it is shown that he who has solved the half space Dirichlet problem for Laplace's equation has already solved the half space Dirichlet problem for the equation In Part 2, the solution formula for the quarter space Dirichlet problem for Laplace's equation is obtained from the Poisson integral formula for the half space Dirichlet problem for Laplace's equation. A representation theorem for harmonic functions in the quarter space is deduced. The method of descent is used, in Part 3, to obtain the solution formula for the quarter space Dirichlet problem for the equation by means of the solution formula for the quarter space Dirichlet problem for Laplace's equation. So that, indeed, it is also shown that he who has solved the quarter space Dirichlet problem for Laplace's equation has already solved the quarter space Dirichlet problem for the " equation" For the sake of completeness and clarity, and for the convenience of the reader, the appendix, at the end of Part 3, contains a detailed proof that the Poisson integral formula solves the half space Dirichlet problem for Laplace's equation. The Bibliography for Parts 1,2, 3 is to be found at the end of Part 1.     

Sparre Andersen模型中破产概率的边界

研究在Andersen Spaxre模型中,当破产概率的初始边界已知的时候,根据更新方程和更新方程中函数的单调性来改进破产概率的边界,并进一步改进了严重损失函数G（x,y）的边界．     

Shadow price principles applied to regulated pricing of natural gas

Inclusion of the shadow prices for natural gas in a dynamic fuels model for the United States shows that the primary reason for the relatively large, fly-up in new marginal gas prices in the early 1980's was the release of the pent-up price effects of the U.S. government's price regulations. In accordance with principles, the shadow price of natural gas fell siginificantly following de-regulation of the highcost gas (section 107) in 1980, which represented the precursor for downward adjustments in marginal wellhead prices of new high-cost gas and drilling activity. The modeling results show that no significant fly-up in new marginal gas prices for lower-cost gas (section 102) is likely to occur in 1985, when its phased de-regulation ends and it is finally de-regulated, because no shadow price precursor currently exists for this gas. Shadow price principles clear up the primary misconceptions with regard to natural gas pricing. This application indicates the significance of shadow price principles for regulated pricing in general.     

Coupled-expanding maps and one-sided symbolic dynamical systems

This paper studies relationships between coupled-expanding maps and one-sided symbolic dynamical systems. The concept of coupled-expanding map is extended to a more general one: coupled-expansion for a transitive matrix. It is found that the subshift for a transitive matrix is strictly coupled-expanding for the matrix in certain disjoint compact subsets; the topological conjugacy of a continuous map in its compact invariant set of a metric space to a subshift for a transitive matrix has a close relationship with that the map is strictly coupled-expanding for the matrix in some disjoint compact subsets. A certain relationship between strictly coupled-expanding maps for a transitive matrix in disjoint bounded and closed subsets of a complete metric space and their topological conjugacy to the subshift for the matrix is also obtained. Dynamical behaviors of subshifts for irreducible matrices are then studied and several equivalent statements to chaos are obtained; especially, chaos in the sense of Li–Yorke is equivalent to chaos in the sense of Devaney for the subshift, and is also equivalent to that the domain of the subshift is infinite. Based on these results, several new criteria of chaos for maps are finally established via strict coupled-expansions for irreducible transitive matrices in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, respectively, where their conditions are weaker than those existing in the literature.     

Representation for the Green’s function of the Dirichlet problem for polyharmonic equations in a ball

We explicitly construct the Green’s function for the Dirichlet problem for polyharmonic equations in a ball in a space of arbitrary dimension. The formulas for the Green’s function are of interest in their own right. In particular, the explicit representations for a solution to the Dirichlet problem for the biharmonic equation are important in elasticity.     

Superconvergence of mixed finite element methods for parabolic problems with nonsmooth initial data

Summary. A semidiscrete mixed finite element approximation to parabolic initial-boundary value problems is introduced and analyzed. Superconvergence estimates for both pressure and velocity are obtained. The estimates for the errors in pressure and velocity depend on the smoothness of the initial data including the limiting cases of data in and data in , for sufficiently large. Because of the smoothing properties of the parabolic operator, these estimates for large time levels essentially coincide with the estimates obtained earlier for smooth solutions. However, for small time intervals we obtain the correct convergence orders for nonsmooth data. Received July 30, 1995 / Revised version received October 14, 1996