Sampled-data distributed protocol for coordinated aggregation of multi-agent systems subject to communication delays

This paper studies the coordinated aggregation problem of a multi-agent system. Particularly, all the agents reach a consensus within a pre-specified target region. However, only a subset of agents have access to this target region, and each agent merely interacts with its neighbors by communication. Moreover, there exist unknown heterogeneous delays in communication channels. The underlying communication topology is characterized by a digraph. To accommodate the practical digital disposal, a sampled-data distributed protocol is proposed, where the sampling is asynchronous in the sense that the sampling periods of distinct agents are heterogeneous. The resulting closed-loop system from the proposed sampled-data distributed protocol is in a hybrid fashion that the continuous system is fed-back by using discrete states at sampling instants. The convergence performance of this hybrid closed-loop system is analyzed based on the contraction theory. More specifically, it is first shown that all the states are coordinated to aggregate within the target region, i.e., coordinated aggregation. With this result, it is next shown that all the states are coordinated towards a consensus, i.e., state agreement. These together guarantee the fulfillment of the concerned coordinated aggregation objective. Finally, a simulation example is given to validate the theoretical results.     

Bifurcations and New Traveling Wave Solutions for the Nonlinear Dispersion Drinfel'd-Sokolov ($D(m,n)$) System

In this paper, we employ the theory of the planar dynamical system to investigate the dynamical behavior and bifurcations of solutions of the traveling systems of the $D(m,n)$ equation. On the basis of the previous work of the reference \cite{zhang}, we obtain the solitary cusp waves solutions (peakons and valleyons), breaking wave solutions (compactons) and other periodic cusp wave solutions. Morever, we make a summary of exact traveling wave solutions to the $D(m,n)$ system including all the solutions which have been found from the references \cite{Deng,Xie,zhang}.     

刚竹毒蛾危害下的毛竹叶片光谱特征及虫害等级检测研究

探讨刚竹毒蛾危害下的毛竹叶片光谱特征可为建立竹林生态安全监测体系提供重要的理论指导。相比于传统的多光谱数据,高光谱遥感能够准确探测不同刚竹毒蛾危害等级间寄主光谱的细微变化。然而,当前有关此方面的研究甚少,其寄主的光谱变化机理还有待进一步总结。为此,基于实测的552条竹叶光谱,分析了健康、受刚竹毒蛾危害、小年叶片之间的光谱差异,选择可反映其健康状况的特征变量,并利用XGBoost模型建立了叶片尺度的刚竹毒蛾危害检测模型。研究结果显示：（1）随着虫害等级的上升,受害叶片在可见光范围内的反射率逐渐出现“绿低红高”的特征,其近红外波段的反射率则不断降低,而短波红外的反射率则明显高于健康叶片,尤其在两个水汽吸收波段（1 450和1 940 nm）的差异最为明显;（2）小年叶片于可见光-近红外波段的反射率显著高于健康、受害叶片;（3）根据不同受害类型叶片的光谱特征可知,较之健康叶片,缺刻型叶片的光谱并未出现太大的变化,红褐色病斑型叶片在红光波段的反射率出现了一定程度的上升,灰白色病斑型叶片则已经完全失去了植被的基本光谱特征;（4）根据XGBoost模型给出的变量重要性排序可知,各特征变量的贡献度依次为PRI（光化学反射率指数）＞FDVI_{576, 717}（植被健康程度评估指数）＞NPCI（归一化色素叶绿素指数）＞DSWI（疾病水胁迫指数）＞VOG 1（红边指数1）＞RVSI（红边植被胁迫指数）＞NDWI（归一化差值水分指数）;（5）模型对刚竹毒蛾危害识别的总平均精度为74.39%,其中健康叶片的识别精度达到了94.55%,轻度危害叶片为74.93%,重度危害为84.12%,小年叶片则为71.10%,而中度危害叶片的识别精度较差,仅为33.48%。     

依据光谱研究闪电回击通道核心的特征参数

闪电回击通道核心中的大电流及其强电磁辐射是引发多种雷电灾害的主要根源。随着现代科技的飞速发展,闪电防护工作显得越为重要。为了完善闪电防护系统,需要从描述闪电回击通道核心的特征参数入手深入研究闪电通道形成和发展过程的微观物理机制。截至目前,光谱观测是获取闪电通道核心特征参数的最佳手段。2015年夏天在青海高原地区的野外试验中,利用由高速摄像机作为记录系统组装的无狭缝光栅摄谱仪,结合快天线地面电场测量仪,记录到一次包括四个回击的云地闪电放电过程的光谱以及与之同步的快电场变化信息。依据光谱,结合等离子体理论计算得到闪电回击通道核心的电导率。在此基础上,应用闪电电动力学模型计算了闪电回击速度、峰值电流、贯穿通道核心的电磁场以及通道核心单位长度的峰值功率等特征参数。结果表明,回击速度在(1.2～2.3)×108 m·s-1的范围内;贯穿回击通道核心的轴向电场、径向电场和磁感应强度的最大值分别在(1.42～1.74)×105 V·m-1,(8.22～9.99)×108 V·m-1和(1.51～2.83) T的范围内。当闪电回击的峰值电流在(7.52～24.05) kA的范围内时,回击通道核心的峰值功率在(0.63～1.92)×109 W·m-1的范围内。另外,分析了电导率、起始电场峰值、回击速度和峰值电流与峰值功率之间的相关性,结果发现峰值电流和峰值功率具有良好的线性关系。研究结果可为探索闪电回击通道形成和发展过程的微观物理机制提供参考依据。     

Improving the non-dominated sorting genetic algorithm using a gene-therapy method for multi-objective optimization

The non-dominate sorting genetic algorithmic-II (NSGA-II) is an effective algorithm for finding Pareto-optimal front for multi-objective optimization problems. To further enhance the advantage of the NSGA-II, this study proposes an evaluative-NSGA-II (E-NSGA-II) in which a novel gene-therapy method incorporates into the crossover operation to retain superior schema patterns in evolutionary population and enhance its solution capability. The merit of each select gene in a crossover chromosome is estimated by exchanging the therapeutic genes in both mating chromosomes and observing their fitness differentiation. Hence, the evaluative crossover operation can generate effective genomes based on the gene merit without explicitly analyzing the solution space. Experiments for nine unconstrained multi-objective benchmarks and four constrained problems show that E-NSGA-II can find Pareto-optimal solutions in all test cases with better convergence and diversity qualities than several existing algorithms.     

SLEk(k>4)��Cardy��ʽ

Cardy给出临界渝流族横穿一个长方形 而不碰到长方形的上边和下边的概率估计公式; Lawler, Schramm和Werner给出了参数的通弦随机Loewner演 变穿过长方形的类似的概率估计公式. 在本文, 我们将后者的结果推广到的情形.     

有界变差函数的加权Ostrowski型不等式的改进及其应用(英文)

本文改进了有界变差函数的加权Ostrowski型不等式,并给出了其在求积公式中的应用.     

Wavelet operational matrix method for solving the Riccati differential equation

A Haar wavelet operational matrix method (HWOMM) was derived to solve the Riccati differential equations. As a result, the computation of the nonlinear term was simplified by using the Block pulse function to expand the Haar wavelet one. The proposed method can be used to solve not only the classical Riccati differential equations but also the fractional ones. The capability and the simplicity of the proposed method was demonstrated by some examples and comparison with other methods.     

Synchronization configurations of two coupled double pendula

We consider the synchronization of two self-excited double pendula hanging from a horizontal beam which can roll on the parallel surface. We show that such pendula can obtain four different robust synchronous configurations. Our approximate analytical analysis allows to derive the synchronization conditions and explains the observed types of synchronizations. We consider the energy balance in the system and show how the energy is transferred between the pendula via the oscillating beam allowing the pendula’ synchronization.     

Threshold analysis of the susceptible-infected-susceptible model on overlay networks

In this paper, we study epidemic spreading on overlay networks in which n multiple sets of links interconnect among the same nodes. By using the microscopic Markov-chain approximation (MMA) approach, we establish the conditions of epidemic outbreak for two kinds of spreading mechanisms in such an overlay network: the concatenation case and the switching case. When a uniform infection rate is set in all the subnetworks, we find the epidemic threshold for the switching case is just n times as large as that of concatenation case. We also find that the overlay network with a uniform infection rate can be considered as an equivalent (in the sense of epidemic dynamics and epidemic threshold) weighted network. To be specific, the concatenation case corresponds to the integer weighted network, while the switching case corresponds to the fractional weighted network. Interestingly, the time-varying unweighted network can be mapped into the static weighted network. Our analytic results exhibit good agreement with numerical simulations.