时变系统线性二次型问题:无约束条件时的一般结果和有控制能量约束条件时的讨论

本文中我们首先对无约束条件时的有限时间区间上时变系统线性二次型(FH-LQ)问题进行了分类,并给出了问题属于每一类的充分必要条件(定理2).其次证明了对于FH-LQ问题其下确界有限与其可达是等价的(定理1).在此基础上给出了问题为正则的一些新的条件(定理3).最后,我们通过新的途径讨论了有控制能量约束时的FH-LQ问题.     

关于文"LQ逆问题研究"的问题讨论

关于文“ＬＱ逆问题研究”的问题讨论傅诒辉（华中理工大学自控系武汉４３００７４）关键词ＬＱ逆问题，加权矩阵，极点配置．文［门定理２给出了连续系统ＬＱ逆问题有解的充分条件以及确定加权矩阵Ｑ和Ｒ的参数化方法．本文构造性地给出了满足文［１］定理２全部条件的参...     

知识概念的模糊模型及模糊目标的识别

作为ＥＢＬ（Ｅｘｐｌａｎａｔｉｏｎ－ＢａｅｓｅｄＬｅａｒｎｉｎｇ）的发展,从概念的自然形成过程出发,提出了一种新的概念模型ＦＥＢＭ（ＦｕｚｚｙＥｘｐｌａｎａｔｉｏｎ－ＢａｓｅｄＭｏｄｅｌ）当概念的解释谓词集中模糊集以及解释谓词取模糊逻辑值时,给出了求概念真值的表达式;为了解决模糊概念的识别问题,引入了概念的模糊解释树ＦＥＴ,接着给出了对象的模糊识别算法ＦＥＢＬ,最后讨论了ＦＥＢＭ与ＦＥＢＬ的可操作     

无约束优化的对角拟牛顿算法

无约束优化的对角拟牛顿算法林梦雄（中国科学院计算中心）首南祺（江西抚州师范专科学校）ＡＤＩＡＧＯＮＡＬＱＵＡＳＩ－ＮＥＷＴＯＮＡＬＧＯＲＩＴＨＭＦＯＲＵＮＣＯＮＳＴＲＡＩＮＥＤＯＰＴＩＭＩＺＡＴＩＯＮ￥ＬｉｎＭｅｎｇ－ｘｉｏｎｇ（ＣｏｍｐｕｔｉｎｇＣ...     

一种新的H~∞─优化方法：梯度方法

提出一种灵活、有效的Ｈ∞－优化方法：梯度方法．利用Ｈ∞－范数与状态空间实现的关系，定义了目标函数ρ（ε，Ｆ），ρ（ε，Ｆ）与Ｈ∞－范数之间的关系是：分析了ρ（ε，Ｆ）的可微性，并给出了ρ（ε，Ｆ）／Ｆ的具体表达式以及使ρ（ε，Ｆ）极大化的梯度方法，从而导致的极小化．实例表明，梯度方法能有效地使ρ（ε，Ｆ）上升，并收敛于驻点或终止于不可微点．     

氟化镧电极再活化机理的讨论

本文推断和验证了旧氟化镧电极在一定浓度的ＮａＯＨ溶液中浸泡一定时间，使ＯＨ＾－与ＬａＦ３单晶膜发生作用，表面形成Ｌａ（ＯＨ）３，同时置换出Ｆ＾－，然后取出电极，用二次去离子水洗掉ＬａＦ３电极表面的ＮａＯＨ，使ＯＨ＾－与ＬａＦ３单晶膜终止反应，再放入二次去离子水中电磁搅拌清洗，掉ＬａＦ３单晶膜表面所浮着的Ｌａ（ＯＨ）３，露出新的ＬａＦ３单晶膜，从而使电极达到再活化。     

LQ最优控制系统加权矩阵Q的一种数值算法

利用ＬＱ最优控制逆问题的参数化解,将求解对称、非负定加权矩阵Ｑ的问题变为一类Ｆ－范数优化问题,给出一种求解ＬＱ最优控制指标函数中的加权矩阵Ｑ的简便而系统的方法。算法的优点在于任意给定一组自变量,通过解这类优化问题就可求得满足闭环特征要求的加权矩阵Ｑ,而且具有良好的收敛性。     

频率响应与谱函数对输出自相关矩阵的影响

通过线性时不变系统的平稳序列的输出仍为平稳的，其自相关矩阵Ｒｙ（ｎ）是非负定的。文中对Ｒｙ（ｎ）的正定性作了讨论。利用函数的方法，导出了连续函数关于至多具有可列个跳跃点的纯跳跃函数在「ａ，ｂ」上的斯梯阶积分公式。利用所得公式，在系统的频率响应Ｈ（ω）连续且它的零点集Ｈ０与输入序列谱函数Ｆｘ（ω）的跳跃集Гｘ适合Гｘ∩Ｈ０＝Φ的条件下，证明了输出序列谱函数Ｆｙ（ω）为「－π，π」上的纯跳跃函数的充要     

带有不确定参数的线性时滞系统的强鲁棒H∞-控制:LMI方法

利用线性矩画不等式（ＬＭＩ）方法讨论了带有不确定参数,而且被调输出含时滞状态和干扰输入的线性时滞系统的强理棒Ｈ∞－控制问题,得到了这类系统鲁棒Ｈ∞－控制问题有解的充分必要条件,并且相应给出所有可参数化无记忆强鲁棒Ｈ∞－控制器的设计。     

时变系统中数字LQG自动调节器和跟踪器的计算方法

数字ＬＱＧ自动调节器和跟踪器提供了包含数据采样、分段常数控制及积分准则的实数字控制（ｒｅａｌｄｉｇｉｔａｌｃｏｎｔｒｏｌｐｒｏｂｌｅｍｓ）的求解方法。已有的各种文献对数字ＬＱ，自动调节器数值计算的讨论只限于非时变系统和有关准则（指标）矩阵等范畴。非线性随机系统对状态轨迹的控制往往是通过基于轨进线性化动力学理论的ＬＱＧ自动调节器来完成的，该调节器构成一个时变系统。本文给出了时变系统及时变指标矩阵的数字ＬＱＧ自动调节器及跟踪器的一种计算方法，最后给出了一个计算实例。     

Distance measures for point sets and their computation

We consider the problem of measuring the similarity or distance between two finite sets of points in a metric space, and computing the measure. This problem has applications in, e.g., computational geometry, philosophy of science, updating or changing theories, and machine learning. We review some of the distance functions proposed in the literature, among them the minimum distance link measure, the surjection measure, and the fair surjection measure, and supply polynomial time algorithms for the computation of these measures. Furthermore, we introduce the minimum link measure, a new distance function which is more appealing than the other distance functions mentioned. We also present a polynomial time algorithm for computing this new measure. We further address the issue of defining a metric on point sets. We present the metric infimum method that constructs a metric from any distance functions on point sets. In particular, the metric infimum of the minimum link measure is a quite intuitive. The computation of this measure is shown to be in NP for a broad class of instances; it is NP-hard for a natural problem class. Received: 1 July 1994 / 9 November 1995     

The singular minimum entropy H∞ control problem

In this paper we search for controllers which minimize an entropy function of the closed loop transfer matrix under the constraint of internal stability and under the constraint that the closed loop transfer matrix has H_∞ norm less than some a priori given bound γ. We find an explicit expression for the infimum. Moreover, we give a characterization when the infimum is attained (contrary to the regular case, for the singular minimum entropy H_∞ control problem the infimum is not always attained).     

Inf–sup control of discontinuous piecewise affine systems

This paper considers the worst‐case optimal control of discontinuous piecewise affine (PWA) systems, which are subjected to constraints and disturbances. We seek to pre‐compute, via dynamic programming, an explicit control law for these systems when a PWA cost function is utilized. One difficulty with this problem class is that, even for initial states for which the value function of the optimal control problem is finite, there might not exist a control law that attains the infimum. Hence, we propose a method that is guaranteed to obtain a sub‐optimal solution, and where the degree of sub‐optimality can be specified a priori. This is achieved by approximating the underlying sub‐problems with a parametric piecewise linear program. Copyright © 2008 John Wiley & Sons, Ltd.     

On the equivalence of some transductions involving letter to letter morphisms on regular languages

Summary Equivalence problems of some transductions involving letter to letter morphisms on regular languages are discussed. In particular, we deal with finite substitutions and inverses of finite substitutions. Our main results are the following: (i) The equivalence problem of inverses of finite substitutions on regular languages is undecidable, (ii) The existential equivalence problem of finite substitutions on regular languages is undecidable, and (iii) The length-equivalence problem of finite substitutions on regular languages is decidable.     

Decidability Equivalence between the Star Problem and the Finite Power Problem in Trace Monoids

In the last decade, research on the star problem in trace monoids (is the iteration of a recognizable language also recognizable?) has pointed out the importance of the finite power property to achieve partial solutions to this problem. We prove that the star problem is decidable in some trace monoid if and only if, in the same monoid, it is decidable whether a recognizable language has the finite power property. Intermediate results allow us to give a shorter proof for the decidability of the two previous problems in every trace monoid without a C4 submonoid. We also deal with some earlier ideas, conjectures, and questions which have been raised in the research on the star problem and the finite power property, e.g., we show the decidability of these problems for recognizable languages which contain at most one non-connected trace. Received April 29, 1999, and in revised form November 8, 2000 and in final form November 24, 2000. Online publication February 26, 2001.     

Formalizing Calendars with the Category of Ordinals

Starting from the basic notion of chronology, we provide a natural representation of calendars and appropriate tools for manipulating them, inside the framework of finite ordinals category. We show that calendars are closed under infimum and supremum operations but not under direct limits.     

Stabilized low-order finite elements for frictional contact with the extended finite element method

Contact problem suffers from a numerical instability similar to that encountered in incompressible elasticity, in which the normal contact pressure exhibits spurious oscillation. This oscillation does not go away with mesh refinement, and in some cases it even gets worse as the mesh is refined. Using a Lagrange multipliers formulation we trace this problem to non-satisfaction of the LBB condition associated with equal-order interpolation of slip and normal component of traction. In this paper, we employ a stabilized finite element formulation based on the polynomial pressure projection (PPP) technique, which was used successfully for Stokes equation and for coupled solid-deformation–fluid-diffusion using low-order mixed finite elements. For the frictional contact problem the polynomial pressure projection approach is applied to the normal contact pressure in the framework of the extended finite element method. We use low-order linear triangular elements (tetrahedral elements for 3D) for both slip and normal pressure degrees of freedom, and show the efficacy of the stabilized formulation on a variety of plane strain, plane stress, and three-dimensional problems.     

改进的H-最佳灵敏度的连续性

为克服灵敏度及其加权型极小问题的局限性,本文采用改进形式,即所谓改进的灵敏度极小问题。它允许原系统对象是严格真有理,同时反馈补偿器是真有理传递函数。证明其极小值的存在性和具备连续性。结果表明所采用的性能指标具有适定性。     

Real options pricing by the finite element method

Real option pricing problems in investment project evaluation are mostly solved by the simulation-based methods, the lattice methods and by the finite difference method (FDM). Only a few applications of the finite element method (FEM) to these problems have been reported in the literature; although it seems to be an alternative tool for pricing real options.Unlike the existing finite element-based papers, in this paper we use residual formulation and provide a detailed scheme for practical implementations. The FEM is introduced and developed as a numerical method for real options pricing problems. First of all, a partial differential equation (pde) model is defined, then the problem’s domain is discretized by finite elements. The weak formulation of the pde is then obtained, and finally the solution to the real option pricing problem is found by solving an algebraic system. For benchmarking purposes, the FEM is applied to known investment and abandonment option problems found in the literature and the results are compared with those of some traditional methods. These results show a good performance of the FEM and its superiority over the FDM in terms of convergence, and over the simulation-based methods in terms of the optimal exercise policy.     

Zero cancelling compensators for singular control problems and their application to the inner–outer factorization problem

Many control problems fall into the category of what we call singular control problems, i.e., problems for which known solutions fail owing to the fact that the relevant transfer functions have zeros on the extended imaginary axis, ??^0e. An example of this is the inner–outer factorization (IOF) problem for such transfer functions. In this paper, we show how to design compensators which would allow for a direct solution to these problems through cancellation of the offending ??^0e zeros. This is demonstrated for the IOF problem mentioned above. Our interest lies primarily with infinite zeros but we develop formulae for finite ??^0e compensators as well. The paper also presents some discussions on the infinite zero structure of linear time-invariant systems.