Designing robustly stabilising controllers for LTI spatially distributed systems using coprime factor synthesis

This paper considers the design of feedback controllers for linear, time-invariant, spatially distributed systems in an approach which generalises the H^∞-framework and in particular the H^∞ loop-shaping method. To this end, we introduce a class of spatially distributed system models called finite dimensional, distributed, linear, time-invariant systems. Sensors and actuators are considered to be part of the controller, rather than part of the plant, and thus the controller we wish to design is itself a spatially distributed system. Optimising over placements and shapes of the sensor and actuator spatial distribution functions is an integrated part of the controller design procedure. As an illustrative design example, we present the feedback stabilisation of an electrostatically destabilised, electrically conducting membrane.     

On the H fixed-lag smoothing: how to exploit the information preview

The problem of the continuous-time H^∞ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H^∞ filtering occur is clarified. It is shown that the H^∞ smoother exploits the information preview in an “H² manner”.     

Finding Optimal Ordering of Sparse Matrices for Column-Oriented Parallel Cholesky Factorization

In this paper, we consider the problem of finding fill-preserving sparse matrix orderings for parallel factorization. That is, given a large sparse symmetric and positive definite matrix A that has been ordered by some fill-reducing ordering, we want to determine a reordering that is appropriate in terms of preserving the sparsity and minimizing the cost to perform the Cholesky factorization in parallel. Past researches on this problem all are based on the elimination tree model, in which each node represents the task for factoring a column, and thus, can be seen as a coarse-grained task dependence model. To exploit more parallelism, Joseph Liu proposed a medium-grained task model, called the column task graph, and showed that it is amenable to the shared-memory supercomputers. Based on the column task graph, we devise a greedy reordering algorithm, and show that our algorithm can find the optimal ordering among the class of all fill-preserving orderings of the given sparse matrix A.     

大数质因子分解的量子算法

量子质因子分解算法是一种利用波的特性在量子环境下进行整数质因子分解的新方法。本文首先介绍了量子质因子分解的基本思想及其相关概念，然后分析并给了了大数质因子分解的量子算法，最后对量子算法的发展前景进行了展望。     

一种多重密钥共享认证方案

给出了一种多重密钥共享认证方案．在该方案中，管理者容易给出任意用于共享的多重密钥集，成员拥有的子密钥不仅能重复使用，而且是可认证的．所给方案提供了抵御管理者欺骗和成员欺骗的解决方法．该方案的安全性取决于求解因子分解问题与离散对数问题的计算难度．所给方案与已有方案相比具有明显的优越性．     

多项式函数型回归神经网络模型及应用

文中利用回归神经网络既有前馈通路又有反馈通路的特点，将网络隐层中神经元的激活函数设置为可调多项式函数序列，提出了多项式函数型回归神经网络新模型，它不但具有传统回归神经网络的特点，而且具有较强的函数逼近能力，针对递归计算问题，提出了多项式函数型回归神经网络学习算法，并将该网络模型应用于多元多项式近似因式分解，其学习算法在多元多项式近似分解中体现了较强的优越性，通过算例分析表明，该算法十分有效，收敛速度快，计算精度高，可适用于递归计算问题领域，该文所提出的多项式函数型回归神经网络模型及学习算法对于代数符号近似计算有重要的指导意义。     

一种快速分解大整数的小因子的优化分解树OFT算法

分解大整数的小因子是解决IFP，DLP问题的诸多攻击方法中的重要运算模块．本文在目前分解大整数小因子算法的基础上，提出的优化分解树(Optimized Factorization Tree)算法，利用树型数据结构和相应的构造算法与回溯算法，配合以作者提出的分解表截支方法和优化分组策略，可以将分解大整数小因子的速度提高50％以上．该算法还可以为大整数素性判别做高效过滤，快速识别大部分合数．     

同时镇定问题研究

基于互质分解的状态空间描述，首先得到了可同阶强镇定的充要条件，并给出了一种同阶强定控制器的构造方法，本文证明了２对象同时强镇定可转化为同时强镇定－辅助对象与它的子对象，同阶同时强全２对象等价于同时强镇定一个辅助对象与它的一稳定子对象，同时镇定ｒ＋１个对象等价同时强镇定ｒ－１辅助对象它们的一公共子对象。     

具有完整性的状态反馈H2最优控制器设计

基于互质分解的状态空间描述方法,给出了状态反馈下对执行器失效具有完整性的 H2最优控制器的一种新的参数化形式,将具有完整性H2最优控制器设计转化为设计一严格 正则的稳定控制器同时镇定对应于k个故障状态的k个辅助对象.     

图的(g,f)—因子分解

设Ｇ是一个图，ｇ和ｆ是定义在图Ｇ的顶点集上的两个整数值函数，且ｇ≤ｆ．图Ｇ的一个（ｇ，ｆ）—因子是Ｇ的一个支撑子图Ｈ，使对任意ｘ∈Ｖ（Ｈ）有ｇ（ｘ）≤ｄＨ（ｘ）≤ｆ（ｘ）．若图Ｇ的边集能划分为若干个边不相交的（ｇ，ｆ）—因子，则称Ｇ是（ｇ，ｆ）—可因子化的．给出了一个图是（ｇ，ｆ）—可因子化的一个充分条件，改进了有关结果．