Output feedback controller for polytopic systems exploiting the direct searching of the design space

This paper deals with the problem of designing a robust static output feedback controller for polytopic systems. The current research that tackled this problem is mainly based on LMI method, which is conservative by nature. In this paper, a novel approach is proposed, which considers the design space of the controller parameters and iteratively partitions the space to small simplexes. Then, by assessing the stability in each simplex, the solution space for design parameters is directly determined. It has been theoretically proved that, if there exists a feasible solution in the design space, the algorithm can find it. To validate the result of the proposed approach, comparative simulation examples are given to illustrate the performance of the design methodology as compared to those of previous approaches.     

矩形孔径柱面镜面形拟合基底多项式研究

对矩形孔径柱面镜面形的拟合方法进行了研究,将矩形域的扩展Zernike多项式与Chebyshev多项式分别作为面形拟合基底,对导出面形数据进行波面复原,分析赛德像差与拟合基底的对应关系对比拟合结果,Chebyshev多项式较矩形域的扩展Zernike多项式有较好的像差分离能力。     

Rhombellation: a builder for multi-shell clusters

Rhombellanes are mathematical structures, proposed by us in 2017; they may appear both in periodic crystals or in finite structures. The simplest rhombellane is rbl.5 or K_2.3, the complete bipartite graph. In this paper, rhombellation operation is iteratively applied on three classes of structures: cube, tori and cubic pcu-network, respectively. The structural topological parameters are detailed.     

基于Stacking框架的蓝莓硬度预测可溶性固形物含量及维生素C模型构建

目的 探索了一种基于蓝莓的质量、硬度快速、无损预测它的可溶性固形物与维生素C含量的方法,为蓝莓化学成分的预测提供一种新思路。方法 通过对蓝莓质量、硬度与可溶性固形物（soluble solid content, SSC）含量、维生素C（vitamin c, VC）相关性分析后,建立了基于一维特征的质量和硬度预测SSC与VC模型。其次,对硬度添加多项式特征做升维处理,同一维进行相同研究。最后,对比Stacking框架与单一模型,及添加多项式特征的预测效果。结果 一维特征条件下,基于Stacking框架的硬度预测SSC与VC的R2分别为0.873、0.875,预测效果优于质量与单模型预测;多维特征条件下,硬度添加到3次方时预测SSC效果最佳,R2为0.889,添加到12次方时预测VC含量效果最佳,R2为0.890,预测效果均好于一维特征。结论 Stacking框架结合添加多项式特征在蓝莓硬度快速、无损预测它的SSC及VC方面具有良好的潜力,为蓝莓品质检测提供新途径。     

Reliability-based design optimization of a car body using dimension- reduced Chebyshev polynomial

A reliability-based design optimization (RBDO) method of a car body is presented on basis of dimension-reduced Chebyshev polynomial method (DCM). To improve calculation efficiency and save computational time, complex models are often approximated by metamodels in reliability analysis. Traditional metamodels require a large number of sample points, which is time-consuming. To improve the efficiency, DCM is proposed to approximate the performance function of the car body. First, the performance function is decomposed by the dimension-reduction method into a sum of univariate functions, which are then fitted through Chebyshev polynomials. The reliability of the car body is predicted by the Taylor expansion method and the fourth-moment method. Finally, the result of RBDO is obtained using an improved adaptive genetic algorithm. The proposed method saves on the calculation time with high precision. Besides, the improved adaptive genetic algorithm reduces the number of iterations in the car body optimization and improves the efficiency.     

Nonparametric Autoregression with Multiplicative Volatility and Additive mean

For over a decade, nonparametric modelling has been successfully applied to studying nonlinear structures in financial time series. It is well known that the usual nonparametric models often have less than satisfactory performance when dealing with more than one lag. When the mean has an additive structure, however, better estimation methods are available which fully exploit such a structure. Although in the past such nonparametric applications had been focused more on the estimation of the conditional mean, it is equally if not more important to measure the future risk of the series along with the mean. For the volatility function, i.e. the conditional variance given the past, a multiplicative structure is more appropriate than an additive structure, as the volatility is a positive scale function and a multiplicative model provides a better interpretation of each lagged value's influence on such a function. In this paper we consider the joint estimation of both the additive mean and the multiplicative volatility. The technique used is marginally integrated local polynomial estimation. The procedure is applied to the deutschmark/US dollar daily exchange returns.     

高马赫航空遥感器光学窗口的光机热分析

为了获得航空光学遥感器高质量成像,分析了高马赫飞行下温度和压力对光学窗口光学性能的影响。首先利用有限元分析软件计算出窗口玻璃在指定温度场或压力场和边界条件作用下的变形量;然后根据得到的窗口玻璃表面节点的位移变化,再以Zernike多项式为接口拟合镜面变形,将计算出的Zernike拟合系数带入光学分析软件ZEMAX中进行分析;最后结合某光学系统对比分析了温度场和压力场作用下的光学系统传递函数图。通过对比结果分析可知,高马赫飞行时,窗口玻璃上产生的温度场对光学系统的传递函数的影响比窗口上的压力场大得多。结果表明,高马赫飞行中,窗口玻璃的设计应更多程度的考虑温度影响。此分析可为高马赫工况下光学窗口的设计提供一定参考。     

多项式微分方程的广义反射函数及其周期解

为了研究多项式微分方程周期解的存在性与稳定性,通过多项式微分方程的广义反射函数来寻找其Poincaré映射.给出了多项式微分方程具有线性广义反射函数的充要条件,以及在该条件下线性广义反射函数的具体表达式和多项式微分方程周期解的存在性与稳定性.该结果对研究相关微分方程周期解与稳定性具有一定的参考价值和指导意义.     

多点泰勒展开的渐进构造和显式计算及应用

渐进式构造公式具有渐进性,即假设得到n次逼近阶的n次多项式且需要计算具有n+1次逼近阶的n+1次多项式时,在n次多项式的基础上增加一项新的多项式及其对应的常系数即可,从而极大地简化了相应的计算量,且在多项式逼近等方面有着较重要的应用。该文给出了多点泰勒展开式的渐进式构造方法及其显式公式,并应用于曲线的逼近问题中。数值例子表明,与已有的方法相比,该文方法在次数变化时具有更小的计算量,或更好的逼近效果。     

非负线性最小二乘问题的一种严格可行内点算法

给出了非负线性最小二乘问题的一个新算法。首先,把非负线性最小二乘转化为线性互补问题,结合牛顿方向和中心路径方向,通过求解一个线性方程组得到搜索方向;进而获得了求解非负线性最小二乘问题的一种严格可行内点算法,并证明该算法经过多项式次迭代之后收敛到原问题的一个最优解,数值实验表明此方法是有效的。