P2-Packing问题参数算法的改进

P_2-Packing问题是一个典型的NP难问题.目前这个问题的最好结果是时间复杂度为O(2~(5.301k))的参数算法,其核的大小为15k.通过对P_2-packing问题的结构作进一步分析,提出了改进的核心化算法,得到大小为7k的核,并在此基础上提出了一种时间复杂度为O(2~(4.142k))的参数算法,大幅度改进了目前文献中的最好结果.     

混合H2/H∞参数辨识

研究了混合H₂/H_∞参数辨识问题.将混合H₂/H_∞估计方法应用到系统参数辨识中,给出了混合H₂/H_∞参数辨识算法.所得的算法不仅能满足规定的鲁棒性能,且为最小二乘(LS)参数估计误差判据提供了一个最优上界.结果表明:提高辨识的鲁棒性,需要牺牲辨识的精度作为代价.最后,仿真结果也验证了该方法的有效性.     

基于A2范数的加权低秩子空间聚类

子空间聚类在运动分割、人脸聚类上得了广泛的应用,并且取得很好的聚类效果.针对稀疏子空间聚类和最小二乘回归子空间聚类求得的表示系数存在类内过于稀疏和类间过于稠密的问题,本文利用l₂范数,提出一种基于欧氏距离的且具有组效应的加权低秩子空间聚类算法,此算法通过基于欧氏距离的加权方式,使得最终的表示系数在保证同一子空间数据点联系的同时,减小不同子空间数据点之间的联系.利用此表示系数建立相似矩阵J,将J应用到谱聚类得到聚类结果.实验结果表明,与当前流行的算法比较,本算法取得了较好的聚类效果.     

l1优化在网格去噪中的应用

目的 网格去噪是计算机图形学中的经典问题,而如何在去除噪声的同时保持网格的特征结构是这一研究方向所面临的最大挑战。方法 提出一种具有稀疏性的全局网格去噪方法,该方法源于信号处理理论中稀疏表示的基本思想,通过优化全局能量函数来去除网格模型的噪声,同时能够保持网格模型的特征结构。该方法共分为两个步骤,第1步为网格面法向量的滤波,首先建立全局优化模型,对噪声网格的面法向量进行滤波优化,其中引入l₁范数来保证解的稀疏性,使得优化后新的面法向量能够保持网格的特征结构;第2步为网格曲面的重建,根据第1步得到的新的面法向量,按照面法向量的定义,建立最小二乘意义下的网格顶点的重建模型,求解得到新的网格曲面。结果 由于该模型是全局方法,避免了现有滤波方法可能出现的不收敛等问题,能够取得比较满意的去噪效果。结论 大量实验结果表明,本文方法在去除噪声的同时,能较好地保持网格的特征结构,尤其对于CAD模型有很好的实验效果。     

结合纹理梯度抑制与L0梯度最小化的纹理滤波

目的 纹理滤波是计算机视觉领域的一个基础应用工具,其目标是抑制图像中不必要的纹理细节和保持图像的主要结构。目前已有的纹理滤波方法多存在强梯度纹理无法被抑制或结构丢失的问题,为此提出一种结合纹理梯度抑制与L₀梯度最小化的纹理滤波算法。方法 首先,提出一种能够区分结构/纹理像素的方向性区间梯度算子,其中采取了局部对比度拉伸和尺度自适应策略,提升了弱梯度结构像素的识别能力。随后,利用区间梯度幅值对原始图像梯度进行抑制,并用抑制后的图像梯度进行图像重建,获得纹理像素梯度小于结构像素梯度的纹理抑制图像。最后,考虑到纹理梯度抑制时会对结构像素的梯度产生一定的衰减作用,本文采用具有梯度提升作用的L₀梯度最小化方法对纹理抑制图像进行滤波,得到纹理抑制结构保持的纹理滤波图像。结果 通过测试马赛克和自然风景等不同类型的图片,并与L₀梯度最小化、滚动引导图像滤波、相对总变分、共现滤波等方法相比较,本文算法能够在抑制强梯度纹理的情况下对图像的主要结构得以保持,并且具有良好的普适性和鲁棒性。同时本文将纹理滤波应用于图像的边缘检测和细节增强,取得了不错的效果提升。结论 本文算法在兼顾强梯度纹理的抑制和结构的保持方面已超越已有的方法,对于图像的目标识别、图像融合、边缘检测等易受强梯度纹理干扰的技术领域,具有较大的应用潜力。     

Multi-log2N交换网络的性能分析模型及控制算法

高速多平面交换网络解决了其内部冲突问题,但需要相应的路由控制算法的辅助,否则,内部冲突不能彻底解决.这是因为包在输入级路由平面的选择不够恰当,容易导致路由冲突的产生.因此,根据冲突链路集的思想,给出一种Multi-log₂N交换网络的控制算法.该算法控制分组在路由平面间的选择,不仅能够适用于RNB和SNB,还能实现单播和多播的控制,保障Multi-log₂N完全实现无阻塞.另一方面,Multi-log₂N消除了内部的链路冲突,提高了交换速率,但对其交换性能缺乏系统的理论分析.给出一种基于嵌入式马尔可夫链的分析模型,对Multi-log₂N网络中队列的使用及分组在队列中的平均等待时间、平均队长等相关性能指标进行了系统的分析,为基于Multi-log₂N的光交换节点的设计提供了良好的理论依据.     

结合P张量积压缩感知的混沌图像加密算法

针对目前数据加密算法缺乏隐蔽性的缺点, 提出了一种结合P张量积压缩感知(P-tensor product compressive sensing, PTP-CS)模型和新分段混沌映射(segmented chaotic map, SCM)的视觉安全图像加密算法. 首先, 根据“拉伸和挤压”机制设计出一新的具有分式结构的分段混沌映射, 用以构建受控测量矩阵. 其次, 在测量矩阵和密码流的共同控制下, 明文的小波包系数矩阵经过二维阿诺德置乱、线性测量以及双向异或扩散生成视觉上无语义的中间秘密图像. 然后, 再采用数字隐写编码方法将其随机地嵌入到某一非涉密传输介质中以同步实现对敏感明文数据的内容和视觉的双重保护. 最后, 一系列的仿真实验和安全性分析表明所提加密算法能够抵御多种常见的攻击, 且具有很好的视觉安全性和压缩性能.     

混合H2/H∞鲁棒控制器设计

在状态空间描述下,定义了混合H₂/H_∞控制的完整信息、完整控制、干扰顺馈、输出估计这4种典型情况.在二次稳定意义上,讨论了混合H₂/H_∞的性能指标,及这4种典型情况的混合H₂/H_∞线性反馈控制器设计,给出了充分必要条件.在典型情况分析的基础上,研究一般意义上的混合H₂/H_∞反馈控制器设计.H₂和H_∞的干扰输入阵及性能评价函数各不相同时的混合H₂/H_∞反馈控制器,与H₂和H_∞控制器设计相似,归结为解两个Riccati方程.但这两个Riccati方程含有参数,最优解要通过搜索这两个参数得到.结果包含了单纯的H₂和H_∞设计,可看作是H₂,H_∞和混合H₂/H_∞的统一设计方法.最后通过一个简单的例子,说明了控制器设计方法的可行性.     

客户导向目录分割问题的改进算法

客户导向目录分割问题假设顾客至少对目录中一定数量的商品感兴趣,计算目录覆盖的顾客数量,据此评估目录分割结果. 现有的分割算法为了保证目录尽可能多的覆盖顾客,而忽略了目录分割结果的效用. 针对该问题,本文构建一种新的数据存储结构CFP-Tree用于存储顾客交易数据,并提出一种新的算法Effective-Cover解决目录分割问题. 该算法使用树深度遍历法选择目录产品. 实验结果表明,该算法能够获得更好的目录分割结果.     

时延网络化控制系统的H2/H∞混合控制

针对存在多步随机传输时延的网络化控制系统模型 ,研究了其随机稳定性及H₂/H_∞混合控制问题 .在一定的系统通信控制模式下 ,网络传输时延可以建模为一个马尔可夫随机过程 ,通过增广系统状态的方法将原系统转化为一个具有随机跳变系数的离散系统 ,同时通过建立随机跳变Lyapunov函数 ,构建了满足系统随机稳定的H_∞次优和H₂/H_∞混合控制状态反馈控制器 .该控制器可通过求解一组耦合的矩阵不等式而得 .     

New approaches to robust l2?l∞ and H∞ filtering for uncertain discrete-time systemsfiltering for uncertain discrete-time systems

The problems of robust l ₂−l _∞ and H _∞ filtering for discrete-time systems with parameter uncertainty residing in a polytope are investigated in this paper. The filtering strategies are based on new robust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed l ₂−l _∞ or H _∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.     

Relating H2 and H∞ bounds for finite-dimensional systems

For a linear time invariant system, the infinity-norm of the transfer function can be used as a measure of the gain of the system. This notion of system gain is ideally suited to the frequency domain design techniques such as H_∞ optimal control. Another measure of the gain of a system is the H₂ norm, which is often associated with the LQG optimal control problem. The only known connection between these two norms is that, for discrete time transfer functions, the H₂ norm is bounded by the H_∞ norm. It is shown in this paper that, given precise or certain partial knowledge of the poles of the transfer function, it is possible to obtain an upper bound of the H_∞ norm as a function of the H₂ norm, both in the continuous and discrete time cases. It is also shown that, in continuous time, the H₂ norm can be bounded by a function of the H_∞ norm and the bandwidth of the system.     

Convergent algorithms for frequency weighted L2 model reduction

This paper is concerned with computing an L₂-optimal reduced-order model for a given stable multivariable linear system in the presence of input and output frequency weightings. By parametrizing a class of reduced-order models in terms of an orthogonal projection and using manifold techniques as tools, both continuous and iterative algorithms are derived and their convergence properties are established. As an application, we show that an L₂ optimal reduced-order filter in the closed-loop sense can be computed using these algorithms.     

On the gap between H2 and entropy performance measures in H∞ control design

Recent papers have considered the problem of minimizing an entropy functional subject to an H_∞ performance constraint. Since the entropy is an upper bound for the H₂ cost, there remains a gap between entropy minimization and H₂ minimization. In this paper we consider a generalized cost functional involving both H₂ and entropy aspects. This approach thus provides a means for optimizing H₂ performance within H_∞ control design.     

An equivalence between rational H2 and Hankel-norm approximations

Let H(z) be a given function in H₂ A classical problem in engineering analysis is to find a rational function G (z) ε H₂ degree M say, which is closest to H(z) in 2-norm. This problem is typically approached using the cost function |H(z) − G(z)|₂, in which G(z) is allowed to vary over the set of Mth-order rational functions in H₂ and for which stationary points are sought. We show that each stationary point of degree M of this functional coincides with a weighted Hankel-norm approximant to H(z). The weighting function derives from the outer factor of the error function H(z) − G(z) stationary point of the rational H₂ approximation problem.     

Mixed H2/H∞ multi-channel linear parameter-varying control in discrete time

This paper develops a new method for the synthesis of linear parameter-varying (LPV) controllers in discrete time. LPV plants under consideration have a linear fractional transformation (LFT) representation. In contrast to earlier results which are restricted to single-objective LPV problems, the proposed method can handle a set of H₂/H_∞ specifications that can be defined channel-wise. This practically attractive extension is derived by using specific transformations of both the Lyapunov and scaling/multiplier variables in tandem with appropriate linearizing transformations of the controller data and of the controller scheduling function. It is shown that the controller gain-scheduling function can be constructed as an affine matrix-valued function in the polytopic coordinates of the scheduled parameter, hence is easily implemented on line. Finally, these manipulations give rise to a tractable and practical LMI formulation of the multi-objective LPV control problem.     

On the solution of coupled Riccati equations used in mixed H2 and H∞ optimal control

This paper considers a set of three coupled Riccati equations. The solution of these equations constitutes necessary conditions for mixed H₂ and H_∞ control problems. The main contributions of the paper are related to the conditions under which the solution of these equations is unique as well as to characterize necessary and sufficient conditions for the existence of solutions.     

H2 performance of continuous time periodically time varying controllers

This paper uses a frequency domain approach to the analysis of H₂ performance of continuous time periodically time varying controllers. For control of linear time invariant plants, it is shown that the time varying dynamics of the periodic controller deteriorates the closed-loop system H₂ performance and a linear time invariant controller can be found to provide strictly better H₂ control of the system.