STABILITY OF SWITCHED POLYNOMIAL SYSTEMS

This paper investigates the stability of （switched） polynomial systems. Using semi-tensor product of matrices, the paper develops two tools for testing the stability of a （switched） polynomial system. One is to convert a product of multi-variable polynomials into a canonical form, and the other is an easily verifiable sufficient condition to justify whether a multi-variable polynomial is positive definite. Using these two tools, the authors construct a polynomial function as a candidate Lyapunov function and via testing its derivative the authors provide some sufficient conditions for the global stability of polynomial systems.     

OPTIMAL GLOBAL RATES OF CONVERGENCE OF M－ESTIMATES FOR NONPARAMETRIC REGRESSION

ＯＰＴＩＭＡＬＧＬＯＢＡＬＲＡＴＥＳＯＦＣＯＮＶＥＲＧＥＮＣＥＯＦＭ－ＥＳＴＩＭＡＴＥＳＦＯＲＮＯＮＰＡＲＡＭＥＴＲＩＣＲＥＧＲＥＳＳＩＯＮＳＨＩＰｅｉｄｅ；ＬＩＧｕｏｙｉｎｇ（ＩｎｓｔｉｔｕｔｅｏｆＳｙｓｔｅｍｓＳｃｉｅｎｃｅ，ＡｃａｄｅｍｉａＳｉ...     

基于单目视觉的微型飞行器移动目标定位方法

针对目标在地形高度未知环境中移动的情况,给出一种利用微型飞行器机载单目摄像机进行目标定位的方法。首先,借助光流直方图从当前图像帧中提取出移动目标局部区域内的背景特征点|然后,结合机载微机电系统(micro electro mechanical system, MEMS)/ 全球定位系统(global positioning system, GPS)传感器测量的飞行器位姿和空间平面点成像的单应变换关系,在期望值最大化算法中将背景特征点分类为辅助平面点和非辅助平面点,并估计辅助平面到摄像机光心的距离参数和法矢量参数,从而确定移动目标所处辅助平面的空间平面方程|最后,联立求解目标视线方程和辅助平面方程获得交点坐标,转换到惯性系下完成移动目标的地理定位。实验结果表明,当微型飞行器飞行高度为100 m时,操作人员单次点击移动目标的定位误差在15 m以内。     

三阶离散chirp傅里叶变换研究

多项式信号的参数估计是信号处理领域的重要问题,利用三阶离散chirp傅里叶变换可以对三阶多项式信号进行参数估计。研究三阶离散chirp傅里叶变换。给出了三阶离散chirp傅里叶表达式,分析了三阶离散chirp傅里叶变换和三阶连续chirp傅里叶变换的关系。提出了把三阶离散chirp傅里叶变换分解为频率线性chirp率平面、频率二次chirp率平面、线性chirp率二次chirp率平面的方法。利用此方法分析了三个平面内的主瓣、旁瓣的大小。讨论了不同采样率对三阶离散chirp傅里叶变换性能的影响。计算机仿真结果证明了分析的正确性。     

Generating exact nonlinear ranking functions by symbolic-numeric hybrid method

This paper presents a hybrid symbolic-numeric algorithm to compute ranking functions for establishing the termination of loop programs with polynomial guards and polynomial assignments. The authors first transform the problem into a parameterized polynomial optimization problem, and obtain a numerical ranking function using polynomial sum-of-squares relaxation via semidefinite programming (SDP). A rational vector recovery algorithm is deployed to recover a rational polynomial from the numerical ranking function, and some symbolic computation techniques are used to certify that this polynomial is an exact ranking function of the loop programs. At last, the authors demonstrate on some polynomial loop programs from the literature that our algorithm successfully yields nonlinear ranking functions with rational coefficients.     

无人飞行器Ad hoc网络中基于容错的中继节点配置

针对无人飞行器Ad hoc网络的容错设计需求,采用增加中继节点的方法实现。在二维平面同构网络中,将容错问题转化为边长受限条件下最少数量Steiner点的Steiner树问题。提出了两种基于最小成本子图的中继节点配置算法,以求解最少数量的中继节点及其位置,使改变后的网络拓扑图为顶点2-连通,实现容错。第一种为多项式时间的8-近似算法;第二种为随机近似算法,采用文化基因算法,搜索需要新增加的最小成本强化边组合。仿真结果表明了所提算法的有效性,当网络规模较小和中等时,随机近似算法得到的中继节点数量较少,平均情况下性能较优。     

Factorization for n-D Polynomial Matrices over Arbitrary Coefficient Field

Multivariate(n-D) polynomial matrix factorization is one of important research contents in multidimensional(n-D) systems, circuits, and signal processing. In this paper, several results on n-D polynomial matrices factorization over arbitrary coefficient fields are proved. Based on these results,generalizations of some results on general matrix factorization are obtained for given n-D polynomial matrices whose maximal order minors or lower order minors satisfy certain conditions. The proposed results fit for arbitrary coefficient field and have a wide range of application.     

双目视觉在粒子图像测量中的研究

针对粒子测速系统中空间点立体匹配难、空间信息难以表示的问题,构建了基于双目视觉的三维粒子测速一般模型。模型中提出并采用了分层提取的逐层相关法:即先对三维空间进行二维切分,然后结合粒子图像测速(particle image velocimetry,PIV)技术与粒子追踪测速(particle tracking velocimetry,PTV)技术对不同帧的二维粒子层面进行相关处理并求出粒子运动矢量。最后平面校正实验、空间切片重构实验以及人工合成粒子图的测速试验均证明了该方法的可靠性,使用该方法可以较精确的得到可测范围内空间任意点的矢量场。     

光滑支持向量机多项式函数的研究

为了找到多项式光滑支持向量机(polynomial smooth support vector machine,PSSVM)中性能更好的光滑函数,将正号函数变形并展开为多项式级数,得到一类光滑函数。证明了这类函数的性能,它既能满足任意阶光滑的要求,也能达到任意给定的逼近精度。用Newton-Armijo算法求解相应的PSSVM模型,实验结果表明,随着多项式光滑函数阶数的提高,逼近精度和相应PSSVM模型的分类性能也相应提高。     

The RCH Method for Computing Minimal Polynomials of Polynomial Matrices

In this paper,a randomized Cayley-Hamilton theorem based method(abbreviated by RCH method) for computing the minimal polynomial of a polynomial matrix is presented.It determines the coefficient polynomials term by term from lower to higher degree.By using a random vector and randomly shifting,it requires no condition on the input matrix and works with probability one.In the case that coefficients of entries of the given polynomial matrix are all integers and that the algorithm is performed in exact computation,by using the modular technique,a parallelized version of the RCH method is also given.Comparisons with other algorithms in both theoretical complexity analysis and computational tests are given to show its effectiveness.     

基于SMC的分布式隐私保护数据发布研究

针对垂直分布式存储结构的隐私保护数据发布问题,基于元组等价群的概念给出全局k-匿名化的定义和充要条件,采用集合多项式表示方法求解出全局元组ID等价群;并基于多方安全计算的同态加密协议构建了具有隐私性、准确性和公平性的分布式隐私保护k-匿名模型,从而实现了各微数据提供方不泄露本地隐私信息的前提下由半可信第三发布方发布出可供统计分析和数据挖掘等需求的真实有效数据集。实验结果表明,该模型具有很好的安全性、准确性和适用性。     

Computing the Determinant of a Matrix with Polynomial Entries by Approximation

Computing the determinant of a matrix with the univariate and multivariate polynomial entries arises frequently in the scientific computing and engineering fields. This paper proposes an effective algorithm to compute the determinant of a matrix with polynomial entries using hybrid symbolic and numerical computation. The algorithm relies on the Newton’s interpolation method with error control for solving Vandermonde systems. The authors also present the degree matrix to estimate the degree of variables in a matrix with polynomial entries, and the degree homomorphism method for dimension reduction. Furthermore, the parallelization of the method arises naturally.     

多维向量场特征参数的几何代数统一计算方法

以几何代数多维统一运算为基础, 探讨了多维向量场的多重向量表达与基本运算, 给出了向量场微分的模板卷积计算方法. 利用几何积对内外积的统一表达, 建立散度和旋度的统一计算方法并进行算法实现. 该方法不仅再现了向量场散度和旋度参数的几何关联性及其微分特性, 更实现了多维统一与坐标无关的计算. 基于北美风场的模拟实验显示, 该算法比基于梯度的间接求解算法具有更好的对比度与平滑性特征, 且具有较强的抗噪音能力, 从而可为向量场数据分析提供新的思路与方法基础.     

ON THE CONSTRUCTION OF GROEBNER BASIS OF A POLYNOMIAL IDEAL BASED ON RIQUIER-JANET THEORY

As a consequence of a previons study of algebraic differential geometry(see [WU1]) theremay be associated to certain special kinds of differential ideals some well-behaved basis enjoyingsome well-behaved properties.If the differential ideals are further specialized so that theycorrespond to ordinary polynomial ideals then such a well-behaved basis will become the usualGroebner basis of the polynomial ideals while the latter is not known for differential ideals.     

基于数据域描述的模糊临近支持向量机算法

针对传统支持向量机由于样本中存在孤立点或噪声而导致的过学习问题,通过分析模糊支持向量机和临近支持向量机的特点,借鉴它们的优点:模糊隶属度和临近超平面,提出了一种数据处理方法。该方法考虑了样本点到类中心的距离与样本对分类的贡献率的关系。这种改进使分类更为清晰和准确。结果表明:采用新的模糊隶属度模糊临近支持向量机算法有较高的识别率,但也耗费了较多的训练时间。     

结构误差对阵列天线极化特性的影响分析

研究了阵列天线阵面变形导致的单元极化差异对天线辐射性能的影响。基于变形后单元的位置,通过3次坐标转换,建立了阵列天线全局球坐标系旋转变换到任意指向单元局部球坐标系的一般步骤,以得到单元在全局坐标系下的极化方向图,并在远场叠加的过程中考虑了单元位置误差的影响。通过对9×5元面阵的数值仿真,得到了可供工程参考的结论。     

QUANTITATIVE PROPERTIES OF GREEN EQUIVALENCES ON SPECIAL MONOIDS

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Obtaining exact interpolation multivariate polynomial by approximation

In some fields such as Mathematics Mechanization, automated reasoning and Trustworthy Computing, etc., exact results are needed. Symbolic computations are used to obtain the exact results. Symbolic computations are of high complexity. In order to improve the situation, exact interpolating methods are often proposed for the exact results and approximate interpolating methods for the approximate ones. In this paper, the authors study how to obtain exact interpolation polynomial with rational coefficients by approximate interpolating methods.     

Conversion Technique of Vector Wave Functions:Formulas and Applications

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Application of Sturm Theorem in the Global Controllability of a Class of High Dimensional Polynomial Systems

In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress.Finally, the authors will give some examples to show the application of our results.