An iterative method for suboptimal control of linear time-delayed systems

This article presents a new approach for solving the Optimal Control Problem (OCP) of linear time-delay systems with a quadratic cost functional. The proposed method can also be used for designing optimal control time-delay systems with disturbance. In this study, the Variational Iteration Method (VIM) is employed to convert the original Time-Delay Optimal Control Problem (TDOCP) into a sequence of nonhomogeneous linear two-point boundary value problems (TPBVPs). The optimal control law obtained consists of an accurate linear feedback term and a nonlinear compensation term which is the limit of an adjoint vector sequence. The feedback term is determined by solving Riccati matrix differential equation. By using the finite-step iteration of a nonlinear compensation sequence, we can obtain a suboptimal control law. Finally, Illustrative examples are included to demonstrate the validity and applicability of the technique.     

Improved error bound for multivariate Chebyshev polynomial interpolation

ABSTRACT

Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties which provides tremendous application potential in mathematical finance. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For efficiency, a sharp error bound is essential, in particular for high-dimensional applications. For tensorized Chebyshev interpolation, we present an error bound that improves existing results significantly.     

利用分段三次多项式提取山谷线和山脊线

通过利用分段三次多项式插值法将地形图中的等高线分段来求曲线的表达式,然后对每段上的表达式采取曲率最大值法,得出等高线弯曲变化的特征点,来提取地形图中的山谷线和山脊线,并选取了某一地区的地形等高线图进行了实验,以验证该方法的正确性。     

岩土参数概率密度函数的正交多项式推断

岩土参数的概率密度函数在岩土工程可靠性的分析中有很重要的作用。文章基于数值逼近原理，直接根据试验样本矩，运用勒让德正交多项式来拟合岩土随机参数的概率密度函数。并且用X^2法进行检验，根据有限比较法确定其中的最佳分布概型，在理论上证明该方法的正确性和实用性。通过算例表明，所得到的逼近表达式有很好的拟舍性能，数值计算稳定，可以满足岩土工程可靠性分析的要求。     

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。     

Harmonic modelling of PV systems for probabilistic harmonic load flow studies

Probabilistic harmonic load flow (HLF) is currently enjoying renewed popularity. This is not surprising since in the near future, thousands of photovoltaic (PV) systems will be integrated into distribution systems. However, as yet, there is no model capable of explaining PV harmonic current behaviour in probabilistic HLF studies. To fill this gap, the harmonic modelling of PV systems proposed in this paper has three key points. First, it provides an effective model of the relationship between PV harmonic current emission and background harmonic voltages. Second, it statistically characterises PV harmonic currents (relative magnitude and phase angle) at different fundamental‐frequency current output intervals using historical time‐series data. In this statistical characterisation, the first fifth moments of each PV harmonic current are used to accurately approximate the raw probability density function (PDF) by means of the Legendre series. Finally, the third key point of this harmonic modelling is a method capable of determining the distribution functions of PV harmonic currents (absolute magnitude and phase angle), based on the statistical characterisation and a fundamental‐frequency probabilistic PV model. The numerical results obtained confirm the effectiveness of this PV model. Copyright © 2014 John Wiley & Sons, Ltd.     

基于广义多项式混沌法的电力系统随机潮流

近年来,随着风、光电源的大量接入,系统运行的不确定性增大,考虑了系统运行随机因素的随机潮流受到更广泛的关注。提出了一种基于广义多项式混沌法的电力系统随机潮流计算方法。该方法利用广义多项式混沌法的正交多项式逼近思想,将系统的随机性分离至正交多项式基,并利用直角坐标潮流方程的二次性避免非线性潮流方程展开的高阶截断误差,进而利用随机Galerkin法,将随机潮流方程转换为一组确定性方程,通过此方程的求解获得随机潮流状态变量的正交多项式逼近系数,由此系数可获得相关变量的期望和方差,并可结合蒙特卡洛仿真,获得变量的概率密度。IEEE 9节点系统的算例表明,该方法的计算误差大致随多项式逼近阶数的上升而指数下降,通常条件下三阶逼近即可获得较高的精度,具有比蒙特卡洛仿真法更高的计算效率。     

小波分析中一类滤波器的构造

通过对多分辨分析性质的讨论,提出了使用数值方法修正初始滤波器得到紧支集正交滤波器的方法。可以针对任何紧支集滤波器进行迭代,自动得到消失矩更高、质量更优的滤波器。基于Legendre多项式,构造一组平移正交系,在得到初始滤波器后进行修正,获得消失矩为2的滤波器。与db3小波进行处理一维信号和二维信号的对比检测,实验证明该滤波器在图像边缘处理中有效。     

基于MATLAB Robotics Toolbox的UR5机器人轨迹规划与仿真

为了解UR5机器人实时轨迹变化情况,根据Denavit-Hartenberg参数法在MATLAB Robotics Toolbox中利用Link函数建立了UR机器人的三维数学模型,对UR5机器人进行了正、逆运动学求解与理论分析,推导出各个关节角之间的变化关系;利用三次多项式插值法对任意PTP (点到点)之间的空间轨迹规划进行理论分析,并结合MATLAB Robotics工具箱对UR5机器人数学模型进行了空间轨迹规划和仿真,得到了连续变化的轨迹曲线。仿真结果验证了机器人运动学模型的正确性和合理性,为UR系列机器人的进一步研究和应用提供了理论依据。     

Construction of a polynomial invariant annihilation attack of degree 7 for T-310

Abstract

Cryptographic attacks are typically constructed by black-box methods and combinations of simpler properties, for example in [Generalised] Linear Cryptanalysis. In this article, we work with a more recent white-box algebraic-constructive methodology. Polynomial invariant attacks on a block cipher are constructed explicitly through the study of the space of Boolean polynomials which does not have a unique factorisation and solving the so-called Fundamental Equation (FE). Some recent invariant attacks are quite symmetric and exhibit some sort of clear structure, or work only when the Boolean function is degenerate. As a proof of concept, we construct an attack where a highly irregular product of seven polynomials is an invariant for any number of rounds for T-310 under certain conditions on the long term key and for any key and any IV. A key feature of our attack is that it works for any Boolean function which satisfies a specific annihilation property. We evaluate very precisely the probability that our attack works when the Boolean function is chosen uniformly at random.