Reference governors and maximal output admissible sets for linear periodic systems

ABSTRACT

In this paper, we consider the problem of constraint management in Linear Periodic (LP) systems using Reference Governors (RG). First, we introduce the periodic-invariant maximal output admissible sets for LP systems. We extend the earlier results in the literature to Lyapunov stable LP systems with output constraints, which arise in RG applications. We show that, while the invariant sets for these systems may not be finitely determined, a finitely-determined inner approximation, which is periodically invariant, can be obtained by constraint tightening. We then analyze the geometric and algebraic relationship between these sets and show that these sets are related via simple transformations, implying that it suffices to compute only one of them for real-time applications. This greatly reduces the memory burden of RG (or other similar constraint management strategies), at the expense of an increase in processing requirements. We present a thorough analysis of this trade-off. In the second part of this paper, we present two RG formulations, and discuss their properties and algorithms for their computation. Numerical simulations demonstrate the efficacy of the approach.     

From sustainability to sustainizability

Following the recent introduction of the Sustainability over Sets (SOS) concept as a sustainability analysis tool with broad flexibility in incorporating human input, in this work, the concepts of Sustainizability (SIZ) and Sustainizability over Sets (SIZOS) are introduced, as novel frameworks for sustainable system synthesis. Springing off the conceptual foundation of sustainability, SIZ (and SIZOS) refers to the existence of allowable external actions, and/or design changes that can render sustainable (sustainable over a set) an unsustainable (unsustainable over a set) system. Utilizing earlier mathematical results for SOS, rigorous necessary and sufficient conditions for SIZOS are presented. Two case studies, on a two-dimensional biological waste treatment system, and a three-dimensional food chain system, are then presented to illustrate the developed necessary and sufficient conditions for SIZOS.     

On generic G-prevalent properties and a quantitative K-S theorem for Cr diffeomorphisms of the circle

We will consider a convex subset of a metric linear space and a certain group of actions G on this set, that allow us to define the notion of Haar zero measure on sets that have zero Haar measure for the translation (by adding) invariant HSY prevalence theory. In this way, we will be able to define the meaning of G-prevalent set according to the pioneering work of Christensen. Our setting considers problems which take into account the convex structure and this is quite different from the previous results on prevalence which consider basically the linear additive structure. In this setting, we will show a kind of quantitative Kupka–Smale theorem, and also we generalize a result about rotation numbers which was first considered by J.-C. Yoccoz (and, also by M. Tsujii). Among other things we present an estimation of the amount of hyperbolicity in a setting that we believe was not considered before.     

Persistence of lower dimensional invariant tori in a class of reversible systems

In this paper we prove the persistence of lower dimensional invariant tori for a class of reversible systems without any non-degeneracy condition. In the proof, we use the special nature that the dimension of the frequency ω is 2 and the modified KAM iteration to prove the persistence of lower dimensional hyperbolic invariant tori, but the frequency has some small shifts from small perturbations.     

Waveguide Invariant and Passive Ranging Using Double Element

The sea-trial results indicate that the stable interference structure can be observed in low-frequency continuous spectra sound field.And the equation of the interference striation have been derived in light of the comcept of waveguide invariant, indicating that the striations are a family of quasi hyperbolas. The heading angle φ, waveguide invariant β and r0/v(r0 is the range of the closest point of approach and v is the navigating velocity of target) are estimated by using Hough transform for the image processing of the LOFARgram and bearing-time records. Four passive ranging algorithms based on double element or double array model are proposed. The simulation research shows that the first positioning algorithm should be adopted when the target heading angle is less than 10°; otherwise, the latter three algorithms are used to range, and the larger the heading angle is, the higher the positioning accuracy is. The relative ranging errors of the four methods are less than 10% under the simulation conditions used in this paper.     

基于组合矩特征的舰船目标识别

针对采用一维距离像特征进行舰船目标识别时,大样本需要、算法复杂和效率较低的问题,提出一种利用组合矩特征进行舰船目标识别的方法.首先提取目标距离像的变换不变矩及小波不变矩特征,并且在考虑算法效率及分类器设计的基础上,最终选取共6维特征构造组合矩,作为分类器输入,并利用实测数据对特征进行简化.分析结果表明:经过实测舰船数据验证,所提取的特征克服了姿态、幅度敏感性等特点,能够较好地表征不同类型舰船的差异.算法分类正确率较高,具有较好的工程应用前景.     

基于Gaussian-Hermite矩的旋转运动模糊不变量

目的 模糊图像的分析与识别是图像分析与识别领域的重要方向。有些图像形成过程中成像系统与物体之间存在相对旋转运动,如因导弹高速自旋转造成的制导图像的旋转运动模糊。大多数对于这类图像的识别都需要先对模糊图像进行“去模糊”的预处理,且该类方法存在计算时间复杂度较高及不适定的问题。对此,提出一种直接提取旋转运动模糊图像中的不变特征,用于旋转运动模糊图像目标检索和识别。方法 本文以旋转运动模糊的退化模型为出发点,提出了旋转运动模糊Gaussian-Hermite (GH)矩,构造了一组由5个对旋转变换和旋转运动模糊保持不变性的GH矩不变量组成的特征向量(rotational motion blur Gaussian-Hermite moment invariants,RMB_GHMI-5),可从旋转变换和旋转运动模糊的图像中直接进行目标检索和识别,无需前置复杂的“去模糊”预处理过程。结果 在USC-SIPI (University of Southern California — Signal and Image Processing Institute)数据集上进行不变性实验,对原图进行不同程度的旋转变换叠加旋转运动模糊处理,证明RMB_GHMI-5对于旋转变换和旋转运动模糊具有良好的稳定性和不变性。在两个数据集上与同类4种方法进行图像检索实验比较,在80%召回率下,本文方法维数更少,相比性能第2的特征向量,在Flavia数据集中,高斯噪声、椒盐噪声、泊松噪声和乘性噪声干扰下的准确率分别提高25.89%、39.95%、22.79%和35.80%;在Butterfly Image数据集中,高斯噪声、椒盐噪声、泊松噪声和乘性噪声干扰下的准确率分别提高4.79、7.63%、5.65%和18.31%。同时,在上述8个测试数据集中进行对比实验以验证融合算法的有效性,结果表明本文提出的GH矩和几何矩相融合算法显著改善了图像检索效果。结论 本文提出的RMB_GHMI-5特征向量在旋转变换和旋转运动模糊下具有良好的不变性与稳定性,在图像检索抗噪性能方面表现优异。相比同类方法,本文方法更具实际应用价值。     

基于轮廓分析与三阶不变矩的旋转目标定位算法

为了解决当前图像定位算法在识别旋转与缩放工件目标时,存在定位成功率不高的问题,提出了基于轮廓分析与不变矩特征的旋转目标定位算法.首先,采用自适应二值化对图像进行预处理,并遍历图像轮廓,完成轮廓序列提取与面积计算,实现对杂质干扰的排除.然后构建三阶不变矩,计算逐一计算图像轮廓序列的三阶不变矩特征,从而建立定位度函数,与模板目标的不变矩特征比较,完成对旋转缩放工件目标定位.实验测试结果表明,与当前图像定位算法相比,在面对缩放十旋转干扰时,本算法拥有更高的定位成功率与鲁棒性.     

混沌振子识别轴承早期故障的极半径不变矩判据

现有的基于混沌振子检测轴承故障的方法的关键步骤是混沌振子相态转变判别,目前大多采用李雅普诺夫指数等特征值进行判断,针对其计算过程复杂,耗费时间长的缺点,基于图像识别技术,提出了一种以极半径不变矩参数作为相态转变的识别方法。通过构造Duffing混沌振子,分析了其相态转变与周期策动力的变化关系,证明其用于轴承早期故障识别的可行性;给出了极半径不变矩的定义,并证明在混沌振子相图由混沌运动态向大尺度周期态转变的过程中,随着周期摄动力不断增加,极半径不变矩表现出单调递增的特性;与HU氏不变矩及二维近似熵判别方法进行对比,讨论了极半径不变矩的抗噪声干扰能力;最终,将该方法用于实际搭建的钻机动力头轴承早期故障诊断的试验中。试验结果表明:极半径不变矩可以识别混沌振子相态过程转变,最低检测信噪比达到-36.99dB,且识别准确率也较另外两种方法提高了4%~7%。证明该方法可以用于轴承早期故障识别,具有识别准确率高,抗噪声干扰能力强,计算简便的优点。