On Convergence Rates of Simultaneously Triangularizable Switched Linear Systems

In this note, we introduce the concepts of best case and worst-case convergence rates for switched linear systems. Their connections to the problems of stability and stabilization are briefly discussed. For simultaneously triangularizable switched systems, explicit formulas are presented for the convergence rates in terms of the system eigenvalues.     

均值模型下满足对数级收敛速度的动态系统

文章研究了在均值模型下,动态系统收敛至一致性状态所需的时间。在每一时间步内,节点计算其邻居的均值,并以计算结果作为自己的新值。我们考虑了当节点间的网络结构处于动态变化状态的情况。我们的分析证明了当节点的度在相邻时间点之间变化较小的情况下,即使仅满足微弱的连通性条件,动态变化的网络仍然可以保证动态系统会快速收敛到一致性状态。     

一类非线性动态系统的非参数GFRF模型辨识

本文对一类用多项式描述的非线性动态系统提出使用ＧＦＲＦ模型类的非参数辨识算法，这种算法的显著特点是需要很小的计算量和存储空间，而且辨识精度较高，仿真结果表明这种非参数模型辨识算法是有效的，而且由辨识方法获得的模型一般具有很好的泛化能力，因而是一种具有重要应用前景的实用方法 。     

Ellipsoidal State Estimates of Linear Dynamic Systems: Their Limiting Behavior

In guaranteed estimation of the states of dynamic systems under deterministic bounded disturbances, use of made of outer ellipsoidal estimates that are optimal relative to the volume and sum of squares of the semiaxes of the ellipsoid. The boundedness and convergence of a sequence of such ellipsoids for stable discrete systems are investigated. The asymptotic behavior of these estimates mostly depends on the minimality criterion chosen for the ellipsoid dimension.     

Verification of Reduced Convergence Rates

In this short article, we recalculate the numerical example in Kíek and Neittaanmäki (1987) for the Poisson solution u=x(1–x)siny in the unit square S as . By the finite difference method, an error analysis for such a problem is given from our previous study by where h is the meshspacing of the uniform square grids used, and C₁ and C₂ are two positive constants. Let =u–u_h, where u_h is the finite difference solution, and is the discrete H¹ norm. Several techniques are employed to confirm the reduced rate of convergence, and to give the constants, C₁=0.09034 and C₂=0.002275 for a stripe domain. The better performance for arises from the fact that the constant C₁ is much large than C₂, and the h in computation is not small enough.     

Estimates of the Real Structured Radius of Stability of Linear Dynamic Systems

A question is examined as to estimates of the norms of perturbations of a linear stable dynamic system, under which the perturbed system remains stable in a situation where a perturbation has a fixed structure.     

Approaches to Robust Filtering Design of Discrete Time Fuzzy Dynamic Systems

This paper presents two filter design methods for discrete time fuzzy dynamic systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting filtering error system is globally stable with guaranteed H_infin or generalized H₂ performance and the filter gains can be obtained by solving a set of linear matrix inequalities. Two simulation examples are also given to illustrate the performance of the proposed approaches.     

Choice of Weighting for Averaged Nonparametric Transfer Function Estimates

The statistical properties of nonparametric transfer function estimates formed via the weighted sum of empirical transfer function estimates are considered. In the case that the system input is considered deterministic, it is shown that the weighting corresponding to the classical averaged periodogram estimate is optimal. A similar asymptotic result is derived for the case where the input is considered stochastic.     

粒子滤波算法中的有限收敛界

在已有的关于粒子滤波(PF)收敛性研究的成果上,指出了其在工程实践中存在的问题;根据粒子滤波在实际应用中普遍存在的收敛现象,提出了粒子滤波算法的有限收敛界(LCB)的概念,并针对一个经典的非线性滤波估计例子,给出了关于自举PF、裂变自举PF、高斯PF、无味高斯PF和辅助变量PF这5种典型粒子滤波算法有限收敛界的计算结果.LCB既可作为粒子滤波算法性能的度量指标之一,也可作为工程应用中某种粒子滤波算法粒子数选取的一个参考值.     

具有非参数化不确定系统的无偏辨识

本文研究了具有参数和非参数不确定性系统的集员辨识问题：分析表明利用我们在文（５）中提出的ＢＥＬＳ方法可以消除集员辨识中观测噪声引起的偏差，文中通过对系统输入数据的预滤波将已知零点嵌入系统，利用这些零点提供的信息将观测噪声引起的辨识偏差予以消除。     

复杂系统的非参数决策模型

本文针对烧结过程不确定性大,缺乏足够的结构信息,含有大时滞和变时滞等特点,提出用非参数决策“黑箱“模型来研究复杂系统参数间的制约关系。实例表明,所设计的分类器效果良好,推断烧结矿质量的正确率达８１．５％。该模式识别系统具有普遍的工程应用价值。     

协同过滤算法在推荐系统中的应用

介绍了协同过滤算法,并对算法进行了改进,解决了用户稀疏的情况下传统算法的不足,同时通过引入评分阈值,显著提高了个性化协同过滤算法的推荐精度。     

Stabilization of Nonlinear Dynamic Systems Using the System State Estimates Made by the Asymptotic Observer

Consideration was given to asymptotic stabilization of the equilibria of nonlinear dynamic systems using the dynamic output feedbacks, that is, the feedbacks in the estimate of system state made by the asymptotic observer. Presented were the basic methods of constructing the asymptotic observers for the nonlinear dynamic systems with control and the approaches to system stabilization using the system state estimate made by the observer.__________Translated from Avtomatika i Telemekhanika, No. 7, 2005, pp. 3–42.Original Russian Text Copyright © 2005 by Golubev, Krishchenko, Tkachev.This work was supported by the Russian Foundation for Basic Research, project no. 05-01-00840, Grant for State Support of the Leading Scientific Schools, project no. NSh-2094.2003.1, and project no. UR.03.01.141 of Section 1.2 “Russian Universities” of the Subprogram “Basic Research” of the Departmental Scientific Program “Development of the Scientific Potentialities of the Higher School” of the Federal Education Agency of the Russian Federation.     

Convergence of Delayed Dynamical Systems

In this paper, we point out that the conditions given in [1] are sufficient but unnecessary for the global asymptotically stable equilibrium of a class of delay differential equations. Instead, we prove that under weaker conditions, it is still global asymptotically stable.     

On Convergence of External Ellipsoidal Approximations of the Reachability Domains of Discrete Dynamic Linear Systems

The ellipsoid technique is widely used in the guaranteed estimation for approximation of the reachability domains of dynamic systems. The present paper considered the issues of external ellipsoidal estimation of the current and limiting reachability sets of a stable discrete dynamic linear system. Recurrent estimation algorithms using the criterion of minimum trace of the weighted ellipsoid matrix were developed for these systems, and their limiting properties were considered.     

协同过滤推荐系统综述

随着互联网和信息计算的飞速发展,衍生了海量数据,我们已经进入信息爆炸的时代。网络中各种信息量的指数型增长导致用户想要从大量信息中找到自己需要的信息变得越来越困难,信息过载问题日益突出。推荐系统在缓解信息过载问题中起着非常重要的作用,该方法通过研究用户的兴趣偏好进行个性化计算,由系统发现用户兴趣进而引导用户发现自己的信息需求。目前,推荐系统已经成为产业界和学术界关注、研究的热点问题,应用领域十分广泛。在电子商务、会话推荐、文章推荐、智慧医疗等多个领域都有所应用。传统的推荐算法主要包括基于内容的推荐、协同过滤推荐以及混合推荐。其中,协同过滤推荐是推荐系统中应用最广泛最成功的技术之一。该方法利用用户或物品间的相似度以及历史行为数据对目标用户进行推荐,因此存在用户冷启动和项目冷启动问题。此外,随着信息量的急剧增长,传统协同过滤推荐系统面对数据的快速增长会遇到严重的数据稀疏性问题以及可扩展性问题。为了缓解甚至解决这些问题,推荐系统研究人员进行了大量的工作。近年来,为了提高推荐效果、提升用户满意度,学者们开始关注推荐系统的多样性问题以及可解释性等问题。由于深度学习方法可以通过发现数据中用户和项目之间的非线性关系从而学习一个有效的特征表示,因此越来越受到推荐系统研究人员的关注。目前的工作主要是利用评分数据、社交网络信息以及其他领域信息等辅助信息,结合深度学习、数据挖掘等技术提高推荐效果、提升用户满意度。对此,本文首先对推荐系统以及传统推荐算法进行概述,然后重点介绍协同过滤推荐算法的相关工作。包括协同过滤推荐算法的任务、评价指标、常用数据集以及学者们在解决协同过滤算法存在的问题时所做的工作以及努力。最后提出未来的几个可研究方向。     

Reductions Do Not Preserve Fast Convergence Rates in Average Time

Cai and Selman [CS] proposed the following definition for measuring average computation time: A time function t is T on average over a distribution μ if, for all , , where . This definition results in a modification of Levin's notion of average time [L]. The effect of the modification is to control the rate of convergence of the expressions that define average computation time. With this modification, they proved a hierarchy theorem for average-time complexity that is as tight as the Hartmanis—Stearns [HS] hierarchy theorem for worst-case deterministic time. They also proved that under a fairly reasonable condition on distributions, called condition W, a distributional problem is solvable in average polynomial time under the modification exactly when it is solvable in average polynomial time under Levin's definition. Various notions of reductions, as defined by Levin [L] and others, play a central role in the study of average-case complexity. However, the class of distributional problems that are solvable in average polynomial time under the modification is not closed under the standard reductions. In particular, we prove that there is a distributional problem that is not solvable in average polynomial time under the modification but is reducible, by the identity function, to a distributional problem that is, and whose distribution even satisfies condition W. Received August 26, 1996; revised May 29, 1997.     

Dynamic Event-Triggered Quadratic Nonfragile Filtering for Non-Gaussian Systems: Tackling Multiplicative Noises and Missing Measurements

This paper focuses on the quadratic nonfragile filtering problem for linear non-Gaussian systems under multiplicative noises, multiple missing measurements as well as the dynamic event-triggered transmission scheme. The multiple missing measurements are characterized through random variables that obey some given probability distributions, and thresholds of the dynamic event-triggered scheme can be adjusted dynamically via an auxiliary variable. Our attention is concentrated on designing a dynamic event-triggered quadratic nonfragile filter in the well-known minimum-variance sense. To this end, the original system is first augmented by stacking its state/measurement vectors together with second-order Kronecker powers, thus the original design issue is reformulated as that of the augmented system. Subsequently, we analyze statistical properties of augmented noises as well as high-order moments of certain random parameters. With the aid of two well-defined matrix difference equations, we not only obtain upper bounds on filtering error covariances, but also minimize those bounds via carefully designing gain parameters. Finally, an example is presented to explain the effectiveness of this newly established quadratic filtering algorithm.

     

传递函数估计误差的硬界及其渐近性质

本文讨论带遗忘因子的最小二乘法估计传递函数的误差硬界及其渐近性质.在噪声有界等一定假定下,当样本个数趋向无限时,误差硬界收敛于复平面内的一个圆.