Markov跳变线性奇异摄动系统鲁棒H∞控制

In this paper, we study the robust control for uncertain Markov jump linear singularly perturbed systems (MJLSPS), whose transition probability matrix is unknown. An improved heuristic algorithm is proposed to solve the nonlinear matrix inequalities. The results of this paper can apply not only to standard, but also to nonstandard MJLSPS. Moreover, the proposed approach is independent of the perturbation parameter and therefore avoids the ill-conditioned numerical problems.     

判定矩阵稳定、正定以及为M矩阵的统一简化条件

本文给出了一个判定矩阵稳定,正定以及为Ｍ矩阵的统一简化条件,基于该条件提出的判定方法简化了计算,因而应用十分方便,文中给出三个示例说明了方法的应用。     

A matrix gradient algorithm for identification of parameterized time‐varying parameters

This paper considers the problem of estimating time‐varying parameters which can be parameterized by a series of arbitrary known basis functions. It is shown that this problem is equivalent to the observer design problem for a “matrix” dynamic system. A “matrix” gradient algorithm, which mimics the well‐known “vector” gradient algorithm, is proposed to estimate the unknown matrix. The contribution of this paper is to show that convergence of the proposed matrix algorithm is guaranteed by the persistent excitations of both the regressor and the basis functions. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

实时SAR成像系统矩阵转置方法研究与实现

合成孔径雷达（SAR）是一种高分辨率成像雷达,而矩阵转置是实时SAR成像信号处理中一个很重要的操作,矩阵转置的效率高低将直接决定整个SAR成像信号处理系统的性能。对于矩阵转置,可采用行进列出或列进行出、两页式或三页式转置等方法进行处理,但这些方法处理时间较长,转置效率较低。在现有矩阵转置方法的基础上,提出了一种新的矩阵转置方法。在实际硬件平台上利用提出的矩阵转置方法进行了实时SAR成像处理,所得结果的矩阵转置效率为78%,整个SAR成像处理时间为10秒。测试结果表明,该方法对解决矩阵转置问题是行之有效的。     

概率差别矩阵与不完备信息系统属性约简

差别矩阵的概念是基于粗糙集理论对信息系统进行属性约简的一个重要内容。针对不完备信息系统的属性约简本文提出了一种概率差别矩阵的概念与构造方法，给出了相关的定理。在此基础上提出了一种利用概率差别矩阵对不完备信息系统属性约简的方法，并给出了应用举例。     

Weighted steepest descent method for solving matrix equations

This paper describes iterative methods for solving the general linear matrix equation including the well-known Lyapunov matrix equation, Sylvester matrix equation and some related matrix equations encountered in control system theory, as special cases. We develop the methods from the optimization point of view in the sense that the iterative algorithms are constructed to solve some optimization problems whose solutions are closely related to the unique solution to the linear matrix equation. Actually, two optimization problems are considered and, therefore, two iterative algorithms are proposed to solve the linear matrix equation. To solve the two optimization problems, the steepest descent method is adopted. By means of the so-called weighted inner product that is defined and studied in this paper, the convergence properties of the algorithms are analysed. It is shown that the algorithms converge at least linearly for arbitrary initial conditions. The proposed approaches are expected to be numerically reliable as only matrix manipulation is required. Numerical examples show the effectiveness of the proposed algorithms.     

一种分明矩阵法的推广

属性约简是知识发现的重要研究内容,也是Rough集理论的核心内容之一。目前,最常用的计算所有属性约简方法是Skowron的分明矩阵法。文中在深入研究Skowron分明矩阵法的基础上,对Skowron的分明矩阵法进行了推广,提出了广义分明矩阵的属性约简方法,并给出了运行实例。     

Q-矩阵准规则LDPC码编码器设计方案的研究

本文给出了Q矩阵的定义,找到了一种快速搜索9矩阵的算法,并在此基础上提出一种准规则LDPC码编码器设计方案。该设计方案将奇偶校验矩阵H分解成两个子矩阵,通过对这两个子矩阵结构的设计,构造出H矩阵。本文提出的准规则LDPC码编码器算法具有较低的实现复杂度,为LDPC码编码器的设计提供了最佳选择方案。     

面向定制结构的稀疏矩阵分块方法

稀疏矩阵向量乘是科学计算的核心问题,采用定制结构来加速稀疏矩阵向量乘的执行对提升科学计算性能具有重要意义。针对目前面向定制结构的稀疏矩阵分块方法和表示方法的缺点,提出了稀疏矩阵二维均匀分块方法和相应的表示方法嵌套分块CSR。实验结果表明,提出的稀疏矩阵分块方法和表示方法能够有效减少填零个数。     

不相容决策表全部属性约简计算的一个改进方法

指出在决策表是不相容的情况下，常用的计算全部属性约简（代数意义下）的基于Skowron差别矩阵的分辨函数方法会产生错误的结果．为了解决这个问题，本文引入一个改进的Skowron差别矩阵，给出一个基于新的差别矩阵的分辨函数方法，并从理论上证明了方法的正确性．     

基于低秩表示的非负张量分解算法

为了提高图像分类准确率,提出了一种基于低秩表示的非负张量分解算法。作为压缩感知理论的推广和发展,低秩表示将矩阵的秩作为一种稀疏测度,由于矩阵的秩反映了矩阵的固有特性,所以低秩表示能有效的分析和处理矩阵数据,本文把低秩表示引入到张量模型中,即引入到非负张量分解算法中,进一步扩展非负张量分解算法。实验结果表明,本文所提算法与其他相关算法相比,分类结果较好。     

Compromise point incorporating trade-off ratio in multi-objective optimization

The aims of multi-objective optimization are (1) to find pareto-optimal solutions and (2) to analyze the trade-off between conflicting objectives. This paper proposes an interactive method for solving multi-objective optimization problems using the satisficing trade-off method (STOM). In particular, we introduce a trade-off matrix to quantitatively analyze the trade-off between conflicting objectives. Each element of the trade-off matrix consists of a projection matrix of active constraints and gradients of objective functions. In addition, the compromise point and the compromise solution incorporating the trade-off ratio that the decision-maker desires are defined in this paper. The technique to obtain the compromise point is proposed in this paper. Through numerical examples, the validity proposed method is examined.     

LQ逆问题解的一种有效算法

本文研究了LQ最优控制逆问题解的参数化表示结果和基于这一参数化表示结果的矩阵变换解法。研究的对象是线性时不变离散时间系统。此外,文中还给出了不求解代数矩阵Riccati方程确定系统的最优状态反馈系数矩阵K的方法。     

Solving coupled matrix equations over generalized bisymmetric matrices

In this paper, an iterative algorithm is established for finding the generalized bisymmetric solution group to the coupled matrix equations (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases). It is proved that proposed algorithm consistently converges to the generalized bisymmetric solution group for any initial generalized bisymmetric matrix group. Finally a numerical example indicates that proposed algorithm works quite effectively in practice.     

A group interest-based collaborative filtering algorithm for multimedia information

This paper proposes a collaborative filtering algorithm based on user group interest. A novel co-clustering method (BalClust) and various weighted non-negative matrix factorization algorithms are used in the proposed method. The BalClust method is used to divide the raw rating matrix into clusters, which are smaller than the original matrix. Then, the balance factor is introduced to consider the user weight and the item-based CF (collaborative filtering). To predict the rating of the unknown items in the cluster, the non-negative matrix factorization algorithm was used. The proposed method achieves higher predicting accuracy and efficiency on low dimensional and homogeneous sub-matrices, and the method also reduces the computational complexity by combining the user and item-based CF. Based on the proposed method, this paper proposed an incremental learning method to ensure data accuracy and timeliness to overcome the problem brought by data updates. The experimental results show the proposed methods outperformed traditional CF algorithms, and the completion time is reduced.     

Consensus Of Identical Linear Systems with Communication Delays by Using the Information of Second‐Order Neighbors

This paper studies the consensus protocol using the information of second‐order neighbors in undirected and connected networks of linear systems with communication delays. The feedback matrix which guarantees consensus under both the proposed and the traditional protocol is given; it is shown that with this matrix, the networks under the proposed protocol converge faster than the traditional protocol. Based on this result, the delay sensitivity of the proposed protocol is considered under an assumption about the communication topology. The maximum allowable upper bound of the delays is obtained by solving certain linear matrix inequalities. Two simulation examples are presented to illustrate the effectiveness of the theoretical results.     

基于用户偏好和项目属性的协同过滤推荐算法

协同过滤推荐算法是目前应用最为广泛的个性化推荐方法之一,但传统的推荐算法在计算目标用户邻居集时只考虑用户项目评分矩阵中的具体数值,没有考虑用户偏好以及用户评分与项目属性之间的关系,推荐精度也有待进一步提高。针对这一问题,提出了一种基于用户偏好和项目属性的协同过滤推荐算法(UPPPCF)。本算法在传统的用户项目评分矩阵基础上综合考虑用户偏好以及项目属性,把评分矩阵转变成基于用户偏好的用户项目属性评分矩阵,然后根据这一评分矩阵来计算目标用户的最近邻居集,克服了传统相似性计算方法只依靠用户评分值的不足,同时本文对预测值判定给出了一种有效的度量方法。在 MovieLen 数据集上的实验结果表明,本文提出的UPPPCF算法能够有效弥补传统协同过滤算法中的不足,而且在推荐精度上有了明显的提高。     

基于采样点正交变换的改进CKF算法

针对传统CKF算法在解决高维问题时因非局部采样造成的滤波性能下降问题,基于设计的正交矩阵提出了一种改进的CKF算法。采用多元Taylor级数展开,揭示了CKF虽能解决UKF的数值不稳定性问题,但同时也引入了非局部采样问题这一事实;进一步设计出一种正交变换矩阵,用于对CKF算法中的采样点进行变换,并从理论上证明了提出的改进CKF算法相对于CKF在高维、强非线性等非局部采样问题突出的应用场合具有更高的估计精度。仿真结果验证了算法的有效性。     

Closed-loop subspace identification: an orthogonal projection approach

In this paper, a closed-loop subspace identification approach through an orthogonal projection and subsequent singular value decomposition is proposed. As a by-product of this development, it explains why some existing subspace methods may deliver a bias in the presence of the feedback control and suggests a remedy to eliminate the bias. Furthermore, as the proposed method is a projection based method, it can simultaneously provide extended observability matrix, lower triangular block-Toeplitz matrix, and Kalman filtered state sequences. Therefore, using this method, the system state space matrices can be recovered either from the extended observability matrix/the block-Toeplitz matrix or from the Kalman filter state sequences.     

基于Skowron差别矩阵属性约简的矩阵表示

针对目前基于Skowron差别矩阵的属性约简中缺少矩阵表示的问题,定义一种新的矩阵,并给出基于新矩阵的属性约简定义,证明该定义与基于Skowron差别矩阵的属性约简等价。以矩阵为基础,定义属性的重要性,设计一个基于Skowron差别矩阵的属性约简算法,实例证明了算法的有效性。