Spectral approximations of the Stokes problem by divergence-free functions

The method of Moser, Moin, and Leonard (1983) for the approximation of the three-dimensional Navier-Stokes equations using divergence-free subspaces is revisited and analyzed. It is shown that the computed velocity field converges to the physical one with spectral accuracy. Moreover, a method for recovering the pressure field is proposed. This method is stable and provides a pressure that converges to the physical one with spectral accuracy.     

Robust pose invariant face recognition using coupled latent space discriminant analysis

We propose a novel pose-invariant face recognition approach which we call Discriminant Multiple Coupled Latent Subspace framework. It finds the sets of projection directions for different poses such that the projected images of the same subject in different poses are maximally correlated in the latent space. Discriminant analysis with artificially simulated pose errors in the latent space makes it robust to small pose errors caused due to a subject’s incorrect pose estimation. We do a comparative analysis of three popular latent space learning approaches: Partial Least Squares (PLSs), Bilinear Model (BLM) and Canonical Correlational Analysis (CCA) in the proposed coupled latent subspace framework. We experimentally demonstrate that using more than two poses simultaneously with CCA results in better performance. We report state-of-the-art results for pose-invariant face recognition on CMU PIE and FERET and comparable results on MultiPIE when using only four fiducial points for alignment and intensity features.     

Disturbance decoupling of switched linear systems

In this paper, we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version, the exogenous input is considered as the disturbance, in the second, the switching signal and in the third both of them are considered as disturbances. All three versions of disturbance decoupling have direct counterparts for linear parameter-varying (LPV) systems, while the latter instance of the problem is relevant for disturbance decoupling of piecewise linear systems, as we will show. The solutions of the three disturbance decoupling problems will be based on geometric control theory for switched linear systems and will entail both mode-dependent and mode-independent static state feedback.     

一种2R1T类球面并联机构的瞬时速度分析

对一种2R1T（R表示旋转,T表示平移）的类球面并联机构进行了瞬时速度分析. 由于机构的动平台中心与基座中心始终关于过3个球关节的平面对称,利用几何法很容易获得动平台的位置解,然而机构的瞬时速度的计算则相对复杂,尤其是角速度的计算严重依赖姿态矩阵或完整雅克比矩阵的正确求解,并且计算效率低、容易出错. 为此,采用Riemann对称空间理论方法,从机构子链旋量系的对称性出发,建立各子链关节运动的约束,从而简化机构动平台瞬时速度的计算,机构所有可能的瞬时速度组成了一个线性空间,这个空间的基正好解释了机构的瞬时自由度. 最后,给出算例验证了该方法的正确性和有效性. 通过ADAMS（Automatic Dynamic Analysis of Mechanical Systems,机械系统动力学）软件仿真与理论计算对比,角速度误差控制在-0.004~0.006 rad/s以内,线速度误差控制在-0.01~0.015 mm/s以内,采用对称空间理论方法计算瞬时速度用时5.187 s.     

基于多子空间直和特征融合的人脸识别算法

多个子空间直和能保证多个子空间数据融合时多个子空间得到的特征向量相互两两正交,融合数据采用该特征表示时冗余最小,更有利于分类识别。本文基于多子空间直和进行特征融合,提出了一种新的人脸识别算法。通过 2DPCA算法,首先分别计算所有训练样本归一化后正脸、左侧脸及右侧脸图像的协方差矩阵的各P个最大特征值对应的P个相互正交的特征向量,然后通过选取3个子空间的部分满足直 和条件的特征向量组成各自的特征空间(投影空间),再将样本正脸、左侧脸及右侧脸图像分别向各自特征空间投影得到3个特征矩阵,最后将此3个特征矩阵融合为该样本的特征矩阵用于最近邻分类器进行分类识别。最终通过本文3组实验数据的对比说明了该 算法能减少计算量并且提高了识别率。     

A projection method for the numerical solution of linear systems in separable stiff differential equations

This paper deals with the efficient implementation of implicit methods for solving stiff ODEs, in the case of Jacobians with separable sets of eigenvalues. For solving the linear systems required we propose a method which is particularly suitable when the large eigenvalues of the Jacobian matrix are few and well separated from the small ones. It is based on a combination of an initial iterative procedure, which reduces the components of the vector error along to the nondominant directions of J and a projection Krylov method which reduces the components of the vector error along to the directions corresponding to the large eigenvalues. The technique solves accurately and cheaply the linear systems in the Newton's method, and computes the number of stiff eigenvalues of J when this information is not explicitly available. Numerical results are given as well as comparisons with the LSODE code.     

有限维子空间n-自反

本文讨论了L(H)中有限维子空间n-自反与其有限秩算子之间的关系,给出了关于n-自反的定理。     

A complement about almost controllability subspaces

We show that, for any almost controllability subspace, there exist a maximal input chain and a family of state feedbacks which lead to the well known ‘feedback-chain’ expression for this subspace.     

Squaring down LTI systems: A geometric approach

In this paper, the problem of reducing a given LTI system into a left or right invertible one is addressed and solved with the standard tools of the geometric control theory. First, it will be shown how an LTI system can be turned into a left invertible system, thus preserving key system properties like stabilizability, phase minimality, right invertibility, relative degree and infinite zero structure. Moreover, the additional invariant zeros introduced in the left invertible system thus obtained can be arbitrarily assigned in the complex plane. By duality, the scheme of a right inverter will be derived straightforwardly. Moreover, the squaring down problem will be addressed. In fact, when the left and right reduction procedures are applied together, a system with an unequal number of inputs and outputs is turned into a square and invertible system. Furthermore, as an example it will be shown how these techniques may be employed to weaken the standard assumption of left invertibility of the plant in many optimization problems.