基于Gradient-GA的星载赋形天线闭环调零算法

传统的数字信号处理方法如数字波束形成技术在多阵元通道情况下设备量大,而且通道一致性很难保障,导致性能不理想,基于此提出了一种联合梯度和遗传算法的星载天线闭环调零算法,在射频端直接搜索最优权值并完成波束合成,因而不需要多通道数字化处理.该算法结合了遗传算法不受初始值选取的限制,具有全局的搜索的能力和梯度的快速收敛特性,极大地减少了初始种群规模,使运算复杂度大大减小,提高了算法的在线实现能力.通过对其马尔可夫链模型的分析可知该算法以概率1收敛到最优值;基于实测数据的仿真实验表明了该算法的有效性.     

基于混合遗传算法的m序列波形优化设计

现代雷达体制多采用大时宽带宽积的m-序列二相编码脉冲压缩波形,解决信号波形优化问题即使信号波形的脉压比在尽量少损失SNR和主瓣宽度的基础上达到极值.对于m-序列,初始寄存器的选取是关键.对于较长的码,传统的优化方法由于运算量过大造成组合爆炸或陷入局部极值而无法找到最优,传统遗传算法也由于初始种群数的规模运算量比较大,将梯度搜索和遗传算法相结合的混合遗传算法很好的解决了这个问题,通过优化m-序列二相码波形的仿真和性能分析验证了该算法的可行性和有效性.     

基于数据的风能转换系统自适应控制

为了解决风能转换系统的建模困难问题,实现额定风速以下风能捕获率的最大化,根据数据驱动控制理论,在风能转换系统中采用基于数据的自适应控制方法。将风能转换系统用时变动态线性系统合理代替,利用风能转换系统的输入输出数据,通过投影估计算法获取动态线性系统的拟梯度向量,在线调整参与设计出自适应控制器。仿真结果表明采用基于数据的自适应控制方法能够有效地实现额定风速以下风能转换系统的最大风能捕获。     

Knots as Topological Invariants for Gradient-Like Diffeomorphisms of the Sphere S 3

We show how knots in appear in a natural way as complete invariants of topological conjugacy for the simplest gradient-like diffeomorphisms on 3-manifolds.     

2D-Shape Analysis Using Conformal Mapping

The study of 2D shapes and their similarities is a central problem in the field of vision. It arises in particular from the task of classifying and recognizing objects from their observed silhouette. Defining natural distances between 2D shapes creates a metric space of shapes, whose mathematical structure is inherently relevant to the classification task. One intriguing metric space comes from using conformal mappings of 2D shapes into each other, via the theory of Teichmüller spaces. In this space every simple closed curve in the plane (a “shape”) is represented by a ‘fingerprint’ which is a diffeomorphism of the unit circle to itself (a differentiable and invertible, periodic function). More precisely, every shape defines to a unique equivalence class of such diffeomorphisms up to right multiplication by a Möbius map. The fingerprint does not change if the shape is varied by translations and scaling and any such equivalence class comes from some shape. This coset space, equipped with the infinitesimal Weil-Petersson (WP) Riemannian norm is a metric space. In this space, the shortest path between each two shapes is unique, and is given by a geodesic connecting them. Their distance from each other is given by integrating the WP-norm along that geodesic. In this paper we concentrate on solving the “welding” problem of “sewing” together conformally the interior and exterior of the unit circle, glued on the unit circle by a given diffeomorphism, to obtain the unique 2D shape associated with this diffeomorphism. This will allow us to go back and forth between 2D shapes and their representing diffeomorphisms in this “space of shapes”. We then present an efficient method for computing the unique shortest path, the geodesic of shape morphing between each two end-point shapes. The group of diffeomorphisms of S¹ acts as a group of isometries on the space of shapes and we show how this can be used to define shape transformations, like for instance ‘adding a protruding limb’ to any shape.     

基于指数遗忘分布的瞬时频率估计算法

本文提出了基于指数遗忘分布的信号瞬时频率估计算法.与其他的时频分布算法相比,通过采用单边指数分析窗口,指数遗忘分布可以在时频分析中引入迭代算法从而大大提高计算效率,本文对这一算法的性能进行了理论分析,同时其有效性在相应的仿真试验中得到了证明.     

Dirac physical measures for generic diffeomorphisms

We prove that, for a C¹ generic diffeomorphism, the only Dirac physical measures with dense statistical basin are those supported on sinks.     

Symbolic dynamics for normally hyperbolic foliations

We introduce some tools of symbolic dynamics to study the hyperbolic directions of partially hyperbolic diffeomorphisms, emulating the well-known methods available for uniformly hyperbolic systems.     

Local controllability for families of diffeomorphisms

We study groups and semigroups which are generated by analytic families of diffeomorphisms. The central notion is that of local controllability of a family of diffeomorphisms at a given point of the state manifold, which generalizes the familiar notion of local controllability of control systems with continuous, as well as discrete time. Lie theory methods are used. We systematically exploit the so called fast switching variations and properties of the jet spaces of curves on the state manifold.