Hermite matrix in Lagrange basis for scaling static output feedback polynomial matrix inequalities

Using Hermite's formulation of polynomial stability conditions, static output feedback (SOF) controller design can be formulated as a polynomial matrix inequality (PMI), a (generally nonconvex) nonlinear semidefinite programming problem that can be solved (locally) with PENNON, an implementation of a penalty and augmented Lagrangian method. Typically, Hermite SOF PMI problems are badly scaled and experiments reveal that this has a negative impact on the overall performance of the solver. In this note we recall the algebraic interpretation of Hermite's quadratic form as a particular Bézoutian and we use results on polynomial interpolation to express the Hermite PMI in a Lagrange polynomial basis, as an alternative to the conventional power basis. Numerical experiments on benchmark problem instances show the improvement brought by the approach, in terms of problem scaling, number of iterations and convergence behaviour of PENNON.     

A simple method for the inclusion of external and internal supports in the spline finite strip method (SFSM) of buckling analysis

The SFSM is an attractive numerical technique for the buckling analysis of folded-plate structures where general loading regimes and boundary conditions need to be modelled. In implementing splines as interpolation functions in the longitudinal direction of the strip, amended splines have been used conventionally to model the variety of end conditions that may occur. These amended splines are fairly difficult to implement, particularly so if internal restraints are also to be specified. A simple technique for replacing the specification of dedicated amended splines is presented in this paper. The method is then employed to study the local buckling of flat plates under longitudinally and transversely varying compression and bending with different boundary conditions at the ends.     

Computation of approximate optimal policies in a partially observed inventory model with rain checks

This paper proposes a new methodology to solve partially observed inventory problems. Generally, these problems have infinite-dimensional states that are conditional distributions of the inventory level. Our methodology involves linearizing the state transitions via unnormalized probabilities. It then uses an appropriate functional basis to represent the state. Considering the speed and stability of computations, we choose truncated Chebyshev polynomials as the basis. We use Fast Fourier Transforms along with an appropriate discretization of inventory levels to speed up the computations. These main ideas are blended to obtain an iterative algorithm to solve a partially observed inventory model with rain checks. In this model, the inventory manager (IM) does not know the inventory level when it is positive. Otherwise, the IM fully observes it. This model provides a context to illustrate our methodology, which applies to other such models. Although this model has been studied mathematically in the literature, the use of our algorithm provides a numerical approximation of the optimal order quantities. These are compared to the orders released under a base mean-stock policy, where the IM replaces the unobserved inventory level with its mean and applies the well-known base stock policy. We show numerically that the optimal order quantity is very close to the base mean-stock order quantity, when the variance of the inventory distribution is small. When the mean of the inventory distribution is large, the optimal order quantity is more than the base mean-stock quantity, and it is the other way around when the mean is small or negative. These insights are explained via uncertainty and information effects and their interplay. We expect this interplay to show up in other partially observed inventory models.     

On Covering Radius and Discrete Chebyshev Polynomials

 We derive a new upper bound on the covering radius of a code as a function of its dual distance. This bound improves on the Honkala-Litsyn-Tiet?v?inen bound and in a certain interval it is also better than Tiet?v?inen’s bound. Upper bounds on even-weight codes are considered as well. Received: November 4, 1996; revised version: February 1, 1997     

Polynomial Cointegration Between Stationary Processes With Long Memory

Abstract. In this article we consider polynomial cointegrating relationships between stationary processes with long range dependence. We express the regression functions in terms of Hermite polynomials and consider a form of spectral regression around frequency zero. For these estimates, we establish consistency by means of a more general result on continuously averaged estimates of the spectral density matrix at frequency zero.     

Geometric Hermite interpolation with circular precision

We present several Hermite-type interpolation methods for rational cubics. In case the input data come from a circular arc, the rational cubic will reproduce it.     

低矮房屋风致结构响应极值不确定性分析

风致结构响应极值估算在结构抗风的可靠度设计中十分重要。在整个极值估算过程中,由于许多不定或随机的因素存在(如：极值自身、估算方法、样本采集、极值概率模型等),得到的极值通常存在不确定性。在各种影响因素中,该文将考虑结构响应极值变量本身的随机特性,对任意分位点处响应极值的不确定性进行分析。首先,利用有限元软件对低矮房屋模型进行框架结构设计并优化,加载风压荷载得到结构响应时程数据。然后,基于Hermite多项式模型(HPM)转换过程方法,估算得到响应的极值Ⅰ型分布(Gumbel);基于该极值估算方法,提出时程样本偏度、峰度、零超越次数与Gumbel分布两个参数之间的经验公式。接着,考虑前四阶矩的不确定性,利用经验公式以及多步概率分析,对任意分位点处响应极值的不确定性进行估计。最后,给出相关结论。     

Rijndael算法中S盒优化测试方法研究

文章首先说明了Rijndael算法中S盒的四种测试方法,包括差分、线性、雪崩和布尔表达式测试。使用有限域中30个最高次幂为8的不可约多项式利用MATLAB构造不同S盒,然后对这些S盒进行优化测试,发现它们在差分和线性测试上性能相似,在雪崩和布尔表达式测试方面的差别主要在稳定性和分布均匀性上,从这两方面得到了最优的S盒。     

亚纯函数的线性微分多项式分担一个小函数的唯一性

讨论了亚纯函数的线性微分多项式分担一个小函数的唯一性问题,所得定理推广了仪洪勋、杨力的结果.     

LED粘片机运动摆臂的优化设计与分析

LED粘片机在正常工作时,摆臂往往存在运动不平稳、振幅较大及趋稳时间较长等问题,影响粘片效率与精度。通过分析摆臂的整个运动过程,提出新的设计方法。首先,利用5次多项式运动曲线来替代梯形运动曲线,保证摆臂运动过程的平滑性;其次,结合静力学分析、模态分析及瞬态动力学分析,对摆臂进行外形优化设计;然后,为减少摆臂转动惯量对运动的影响,对摆臂进行拓扑优化,得到摆臂的优化模型;最后,通过瞬态动力学分析验证,证实了此方法的可行性。