非部分嵌套信息结构的LQG动态队决策问题的可解性（II）*

本文讨论非嵌套信息结构的递阶队决策问题和控制均享信息结构的LQG分散控制问题,文中首先证明这两类问题的信息结构都是“部分控制嵌入”的,进而给出最优策略(或控制)存在的充要条件和当此条件成立时最优策略(或控制)的表达式。     

A Heuristic Approach to the Discovery of Macro-Operators

This paper describes a heuristic approach to the discovery of useful macro-operators (macros) in problem solving. The approach has been implemented in a program, MACLEARN, that has three parts: macro-proposer, static filter, and dynamic filter. Learning occurs during problem solving, so that performance improves in the course of a single problem trial. Primitive operators and macros are both represented within a uniform representational framework that is closed under composition. This means that new macros can be defined in terms of others, which leads to a definitional hierarchy. The representation also supports the transfer of macros to related problems. MACLEARN is embedded in a supporting system that carries out best-first search. Experiments in macro learning were conducted for two classes of problems: peg solitaire (generalized Hi-Q puzzle), and tile sliding (generalized Fifteen puzzle). The results indicate that MACLEARN'S filtering heuristics all improve search performance, sometimes dramatically. When the system was given practice on simpler training problems, it learned a set of macros that led to successful solutions of several much harder problems.     

Probability densities for conditional statistics in the cubic sensor problem

This paper applies the techniques of Malliavin’s stochastic calculus of variations to Zakai’s equation for the one-dimensional cubic sensor problem in order to study the existence of densities of conditional statistics. Let {X _t} be a Brownian motion observed by a cubic sensor corrupted by white noise, and let denote the unnormalized conditional estimate of φ(X _i ). If φ₁,...,φ _n are linearly independent, and if , it is shown that the probability distribution of admits a density with respect to Lebesgue measure for anyn. This implies that, at any fixed time, the unnormalized conditional density cannot be characterized by a finite set of sufficient statistics. Research supported in part by NSF Grant No. MCS-8301880 and by the Institute for Mathematics and It Applications, Minneapolis, Minnesota.     

曝光数据流优化问题的蒙特卡罗算法

集成工艺中控制图形发生器产生掩模图形的数据流文件的数据排列顺序优化,是一个其结点数可达数千个之多的大规模旅行商问题(从镜头架的位置,即每个矩形的矩心为结点),常规算法早已不适用。本文采用多阶段蒙特卡罗算法并加以改进,补充了“分层优化模式”,邻接结点的预合并和在各个阶段末提取共同子路径并删去相关结点等一系列逐步缩小问题规模的措施,形成了一个实用的优化算法。相应的软件已成功地应用于薄膜磁头的数据流文件的优化。     

A heuristic 0–1 integer programming method

Summary In this paper, we present a novel relaxation method for the integer programming problem:Ax=b,A {–1,0,+1}^m×N,x {0,1}^N, N>m. The report includes experimental results of problems with up tom=100 equations andN=400 variables.     

线性矩阵方程异类约束最小二乘解的迭代算法

多矩阵变量线性矩阵方程(LME)约束解的计算问题在参数识别、结构设计、振动理论、自动控制理论等领域都有广泛应用。本文借鉴求线性矩阵方程(LME)同类约束最小二乘解的迭代算法,通过构造等价的线性矩阵方程组,建立了求多矩阵变量LME的一种异类约束最小二乘解的迭代算法,并证明了该算法的收敛性。在不考虑舍入误差的情况下,利用该算法不仅可在有限步计算后得到LME的一组异类约束最小二乘解,而且选取特殊初始矩阵时,可求得LME的极小范数异类约束最小二乘解。另外,还可求得指定矩阵在该LME的异类约束最小二乘解集合中的最佳逼近解。算例表明,该算法是有效的。     

未知环境下基于约束点的移动机器人路径规划

针对未知环境中障碍物种类多样性和位置不确定性的特点,提出了基于约束点的路径规划方法。首先对机器人在未知环境中检测到的局部障碍物信息进行分类和几何特征属性描述,得其约束点信息,然后引入改进后的A*算法,将其搜索范围局限于约束点上,计算约束点的评价函数值后得到子目标点,机器人到达子目标点后,若陷入死区,则采取回溯路径策略,重新选择子目标点,否则根据该点所属的障碍物种类采取跨越或绕行避障策略,最后移动机器人在未知环境中顺利到达目标点。仿真研究说明本文提出的路径规划方法具有可行性和有效性。     

An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.     

GM模型的几何性质及统计检验

以空间向量几何理论为基础，详细地分析了Ｇａｕｓｓ－Ｍａｒｋｏｖ线性模型的几何性质；在实现了模型图形化描述的基础上，利用各解向量的几何及统计性质构造出了不同情形下的统计检验方法和相应的检验统计量，为全面、深入地研究和灵活运用该模型提出了一种简洁直观的数学方法     

大学生求学满意度实证研究--某高校学生个体特征对满意度单项要素的影响分析

求学满意度，又称为求学满意程度，它取决于教育需求主体对教育服务的预期同其实际所感知的教育服务水平的对比。教学计划、教学组织、教师教学、教学设施、校园环境、学生5知识技能等都是影响求学满意度的因素。本文在调查取得基本数据的基础上，使用相关的统计检验方法，分析了性别、生源地和不同年级这些学生个体地征对求学满意度单项要素的影响。主要结论有：学生性别差异对满意度单项要素的影响基本是随机的；不同生源地的学生对教学计划和管理制度两个要素的评价具有差异；不同年级的学生对教学设施和知识掌握程度的评价具有显著性差异；学生对学校服务评价单项因素差异很少，总体满意度在一定程度上反应学校的实际情况。