透视仿射变换在轴测椭圆中的应用与分析

本文介绍透视仿射交换在轴测椭圆中的应用和作图分析。通过求出对应椭圆的长短轴，可作出实形轴测椭圆。透视仿射交换可用于求两个几何体任意截交线。     

用仿射对应求4点椭圆的方法及应用

本文是应用仿射对应原理,以椭圆曲线上4个点及其中心,求作椭圆的方法。以及用此方法解决某些一般形式的二次曲面中的一些几何作图问题。     

图形生成与图象处理中的仿射变换

在图形生成和图象处理的实际问题中仿射变换是非常有用的，本文用仿射变换讨论了信息复制方法，介绍了分形插值格式与ＩＦＳ方法，强调指出仿射变换可被用来构造一类新的预小波，最后对有关计算机艺术的模型问题给出若干议论。     

线性约束优化的最优路径仿射内点信赖域方法

提供最优路径仿射内点信赖域算法解具有线性等式与线性不等式约束的非线性优化问题。通过在信赖域半径内沿着最优路径搜索求得模型的迭代方向,然后结合非单调内点回代线搜索技术获得可接受的步长因子,从而产生保证目标函数值非单调下降的严格内点可行迭代序列。基于最优路径的良好性质,在合理的假设条件下,可以证明算法不仅具有整体收敛性而且保持超线性收敛速率。引入非单调技术能克服高度非线性的病态问题,加速收敛性进程。     

The Nyquist robust sensitivity margin for uncertain closed‐loop systems

The Nyquist robust sensitivity margin is proposed as a new scalar indicator of robust stability that also provides a meaningful quantitative assessment of the worst sensitivity realized by the uncertain closed loop. After formulating and discussing in detail the underlying optimization problem required for the calculation of the margin, the approach is applied to the characterization of the robust stability of a closed‐loop featuring a linear system with an affine uncertainty structure and a parametric uncertainty set described by a real rectangular polytope. The capabilities of the methodology are illustrated through examples, which include an approach for quantifying alternative robustness margins, such as a parametric stability margin. The computational algorithm is systematic and can be carried out with high numerical precision. Copyright © 2005 John Wiley & Sons, Ltd.     

Identification of piecewise affine systems based on statistical clustering technique

This paper is concerned with the identification of a class of piecewise affine systems called a piecewise affine autoregressive exogenous (PWARX) model. The PWARX model is composed of ARX sub-models each of which corresponds to a polyhedral region of the regression space. Under the temporary assumption that the number of sub-models is known a priori, the input-output data are collected into several clusters by using a statistical clustering algorithm. We utilize support vector classifiers to estimate the boundary hyperplane between two adjacent regions in the regression space. In each cluster, the parameter vector of the sub-model is obtained by the least squares method. It turns out that the present statistical clustering approach enables us to estimate the number of sub-models based on the information criteria such as CAIC and MDL. The estimate of the number of sub-models is performed by applying the identification procedure several times to the same data set, after having fixed the number of sub-models to different values. Finally, we verify the applicability of the present identification method through a numerical example of a Hammerstein model.     

Synthesis of optimal controllers for piecewise affine systems with sampled-data switching

This paper discusses the optimal control problem of the continuous-time piecewise affine (PWA) systems with sampled-data switching, where the switching action is executed based upon a condition on the state at each sampling time. First, an algebraic characterization for the problem to be feasible is derived. Next, an optimal continuous-time controller is derived for a general class of PWA systems with sampled-data switching, for which the optimal control problem is feasible but whose subsystems in some modes may be uncontrollable in the usual sense. Finally, as an application of the proposed approach, the high-speed and energy-saving control problem of the CPU processing is formulated, and the validity of the proposed methods is shown by numerical simulations.     

基于地区电网经济运行的无功综合效益优化

采用地区电网无功综合效益优化模型，从经济运行角度，兼顾地区电网有功网损最小和因数达到要求值，使电网的年运行费用达到最小。优化算法将仿射变换内点法与简化分枝定界法（内点－分枝定界法）综合应用于优化过程中，计算结果表明它是一种有效的无功优化算法。     

Perspective as a Symmetry Transformation

From the quattrocento to the end of the nineteenth century perspective has been the main tool of artists aiming to paint a naturalistic representation of our environment. In painters’ perspective we find a combination of affine projection and similitude. We recognise the original object in the painting because perspective is a symmetry transformation preserving certain features. The subject of the transformation, in the case of perspectival representation, is visible reality, and the transformed object is the artwork. The application of symmetry transformations developed from the origin of perspective through the centuries to the present day. The single vanishing point could be moved (translated), and even doubled, developments that made it possible to represent an object from different points of view. In the twentieth century, the application of topological symmetry combined with similitude resulted in new ways of seeing, new tools for artists such as cubists and futurists.