yl7703永利官网

第一届研究生学术论坛会议通知

为活跃学术氛围，提升学术水平，促进研究生学术创新能力培养，yl7703永利官网拟于11月下旬举办“研究生学术论坛”。该论坛旨在为研究生搭建一个大范围、多领域的学术交流平台，促进研究生之间的学术交流和思想碰撞，通过邀请国内外知名专家的讲座、报告和点评，进行学术熏陶，达到开阔视野，提高创新能力的目的。现将有关内容通知如下：

一、   参与对象

yl7703永利官网全体研究生和教师

二、   活动时间

2020年11月21日

三、   会议形式

1.   邀请报告：拟邀请10名左右知名专家做研究生培养或学术报告；

2.   研究生报告：研三每位学生做学术报告，其它年级鼓励学术报告。

四、   报名申请

请有意参加论坛报告的研究生，于11月15日下午4:30之前将“报名登记表”（见附件）发至学院科研秘书李凯强老师（kaiqiangli19@163.com）。

五、   举办单位

yl7703永利官网

地点：yl7703永利官网 大会议室341

 

yl7703永利官网

第一届研究生学术论坛会议通知

会议日程

2020年11月21日

8：30	开幕式，地点：数学学院341，主持人：陈传军
08:30—09:00	1.        研究生处处长姜付义教授讲话 2.        院长杨玉军教授讲话 3.        合影（数学学院门口） 4.        分组报告开始

 

分组报告1：基础数学方向，会议地点：大会议室341
09:00—10:00	张胜贵（西北工业大学）腾讯会议：664   308 202 Entropies   of graphs, hypergraphs and random graphs
10:00—10:10	茶歇
10:10—11:00	周进鑫（北京交通大学）腾讯会议：664   308 202 Edge-transitive   bi-Cayley graphs
11:00—11:20	于越（yl7703永利官网硕士生） Controllability   of neighborhood corona product networks
11:20—11:40	张星（yl7703永利官网硕士生） 子群完备码
11:40—12:00	蔡晓霞（yl7703永利官网硕士生） 若干指标下图的边连通性问题以及双罗马控制数
15:00—16:00	李靖建（广西大学）腾讯会议：664   308 202 On   the classification of some symmetric graphs

 

分组报告2：控制论方向，会议地点：非线性控制实验室118
09:00—09:50	满永超（山东大学）腾讯会议：281   913 245 Global   practical tracking for nonlinear systems with unknown input powers using dual   high-gain-based adaptive feedback
09:50—10:10	茶歇
10:10—10:50	刘磊（河海大学）腾讯会议：281   913 245 强化学习原理及概述
10:50—11:10	钟鹏（yl7703永利官网硕士生） PUMA560在随机干扰下的抓取控制
11:10—11:30	胡庆羲（yl7703永利官网硕士生） Trajectory   planning and tracking control for 6-DOF Stanford Manipulator based on   adaptive sliding mode multi-stage switching control
11:30—11:50	马开法（yl7703永利官网硕士生） Prescribed   performance control for uncertain flexible-joint robotic manipulators driven   by DC motors

 

分组报告3：计算数学方向，会议地点：小会议室303
09:00—09:50	李剑（陕西科技大学）腾讯会议：100   119 161 浅谈自由流体与多孔介质耦合问题数值方法及其应用研究
09:50—10:10	茶歇
10:10—10:50	晏文璟（西安交通大学）腾讯会议：100   119 161 Shape   optimal design in the incompressible viscous fluids based on the continuous   adjoint method
10:50—11:10	娄玉芝（yl7703永利官网硕士生） 非线性抛物问题和薛定谔问题有限体积元方法高效数值格式
11:10—11:30	王琨（yl7703永利官网硕士生） Unconditionally   energy stable, splitting schemes for  magneto-hydrodynamic equations
11:30—11:50	宫云杰（yl7703永利官网硕士生） 非线性方程的两网格有限体积元方法

 

分组报告4：应用数学方向，会议地点：大会议室341
14:30—15:30	刘衍胜（山东师范大学） 完备性与Baire纲定理及其应用
15:30—15:40	茶歇
15:40—16:30	杨家青（西安交通大学）腾讯会议:    870   709 590 Uniqueness   and numerical methods for inverse scattering by complex obstacles
16:30—16:50	张博（yl7703永利官网硕士生） 一类奇异的Monge-Ampère方程Dirichlet问题解的最优全局渐近行为
16:50—17:10	陈安静（yl7703永利官网硕士生） p-Laplacian椭圆方程大解的全局渐近行为

 

 

 

 

报告摘要

 

Part I. 专家报告

 

浅谈自由流体与多孔介质耦合问题数值方法及其应用研究

李剑 教授（陕西科技大学）

 

基于自由流体与多孔介质耦合问题数值方法及其应用研究，主要从以下几个方面进行简要汇报：

1. 井筒附近的数值方法研究；

2.浅油藏重油混合开采数值模拟；

3. 超重油开采化学新方法数值模拟。

 

 

On the classification of some symmetric graphs

李靖建 副教授（广西大学）

 

The graph is called symmetric graph if its graph automorphism group acts transitive on its vertices and arcs. It is well known that the study of symmetric graphs is a hot topic of algebraic graph theory. In particular, the classification and characterization of such graphs has been closely watched, which is recognized hard but of great theoretical. In this talk, we focus on research the classification of symmetric graphs. In particular, we will introduce some commonly methods and share with you our recent results on the classification of symmetry graphs.

 

 

 

强化学习原理及概述

刘磊 副教授（河海大学）

 

强化学习（Reinforcement Learning），属于一种机器学习架构，它是通过让智能体（Agent）不断地对所处环境（Environment）进行探索和开发并根据反馈的回报（Reward）进行的一种经验学习。2016年,谷歌旗下DeepMind团队发布的AlphaGo以4：1的战绩击败了世界围棋冠军里李世纪石,引爆了强化学习的发展势头。近年来，不论在科研界还是工业界，强化学习发挥重要的作用。本报告简介强化学习的数学原理，以及动态规划、蒙特卡洛、时序差分等基本算法。在时间允许的情况下，将介绍DQN和Actor-Critic等深度强化学习算法。

 

 

完备性与Baire纲定理及其应用

刘衍胜 教授（山东师范大学）

 

本报告先从实数集的完备性讲起，引申出一般距离空间的完备性，重点介绍完备距离空间的一个重要性质--Baire纲定理及其应用。

 

 

Global practical tracking for nonlinear systems with unknown input powers using dual high-gain-based adaptive feedback

满永超 副研究员（山东大学）

 

This talk is devoted to introducing our recent results on global practical tracking for a class of uncertain nonlinear systems. The typical feature of the systems lies in the presence of serious unknowns in the input powers. A novel dual high-gain-based adaptive control design scheme is successfully developed. Remarkably, a dynamic high gain and a high gain function (of system states and adaptive dynamic) are jointly introduced to endow the controller with powerful ability in compensating the serious system unknowns/uncertainties. Under the designed controller, all the signals of the resulting closed-loop system are bounded and furthermore the tracking error can be driven to any prescribed smallness.

 

 

Shape optimal design in the incompressible viscous fluids based on the continuous adjoint method

晏文璟 教授（西安交通大学）

 

In this talk, we will briefly introduce the optimal design of an immersed body in the viscous and incompressible fluid which is driven by the steady-state Navier-Stokes equations. Based on the continuous adjoint method, the structure of shape gradient for the cost functional is derived by the differentiability of a minimax formulation involving a Lagrange functional with the function space parametrization technique. Moreover, a gradient-type algorithm is employed to solve the shape optimization problem. Finally, the numerical examples demonstrate the feasibility and effectiveness of the proposed algorithm.

 

 

Uniqueness and numerical methods for inverse scattering by complex obstacles

杨家青 副教授（西安交通大学）

 

In this talk, I will give an introduction to inverse problems for PDEs, especially for inverse scattering by acoustic, electromagnetic or elastic waves. Then I will report some recent development on inverse problems for wave scattering by complex obstacles, where some interesting uniqueness theorem and inversion algorithms will be represented.

Entropies of graphs, hypergraphs and random graphs

张胜贵 教授（西北工业大学）

 

 The entropy of a graph is defined as the structural information content of the graph. A variety of graph entropies, have been studied extensively and applied to various fields successfully. In this talk, we will introduce some currently popular graph entropies characterizing graphs numerically, and we also present some recent results on these entropies. 

 

 

Edge-transitive bi-Cayley graphs

周进鑫 教授（北京交通大学）

 

A graph admitting a group H of automorphisms acting semi-regularly on the vertices with exactly two orbits is called a bi-Cayley graph over H. This generalisation of a Cayley graph gives a class of graphs that includes many important examples such as the Petersen graph, the Gray graph and the Hoffman-Singleton graph, and most of the known examples are actually edge-transitive. In this talk, I shall introduce some of our recent work regarding edge-transitive bi-Cayley graphs.

 

 

 

 

 

 

 

 

 

Part II. 学生报告

 

若干指标下图的边连通性问题以及双罗马控制数

蔡晓霞

 

   1966年，Chartrand 给出图的最小度足够大时是极大边连通的。后来，很多的数学家借助不同的参量指标分别给出图是极大边连通的充分条件，例如：2009年，Dankelmann 等人依靠逆度、最小度和顶点个数确定一个图是极大边连通的。这里我们主要利用逆度指标（ ）研究图的极大边连通性和超边连通性问题。报告最后会简要介绍一下双罗马控制数。

 

 

p-Laplacian椭圆方程大解的全局渐近行为

陈安静

 

我们主要考虑了p-Laplacian椭圆方程大解的最优全局渐近行为, 这里的是中的有界光滑区域, (或), f在(或)上单调递增且满足Keller-Osserman条件, 且在上为正, 但可能在边界上消失或爆破. 我们赋予了新的结构条件, 它在解决方程大解的全局行为的问题上起到了重要的作用.

 

 

 

 

非线性方程的两网格有限体积元方法

宫云杰

 

In this work, we propose a two-grid finite volume element algorithm based on Crank-Nicolson scheme for nonlinear parabolic equations. This method is considered where the nonlinear problem is solved only on a coarse grid of size  and a linear problem based on the coarse-grid solutions and one Newton iteration is considered on a fine grid of size , which can improve the computing efficiency while keeping the accuracy. It is proved that the two-grid method can obtain asymptotically optimal error estimates in spaces and second order accuracy in time. Meanwhile, a two-grid finite volume element method is proposed for Ginzburg-Landau equation. After the nonlinear problem is solved only on the coarse grid, one Newton iteration is adopted on the fine grid to linearize the fully discrete problem using the corse-grid silution as the initial guess. This method not only keeps the accuracy but also improves the computing efficiency. It is shown that the two-grid method can achieve asymptotically optimal error estimates in -and -norm. Numerical results are provided to verify the theoretical results.

 

 

Trajectory planning and tracking control for 6-DOF Stanford Manipulator based on adaptive sliding mode multi-stage switching control

胡庆羲

 

This paper intends to investigate the trajectory planning and tracking control for six degrees-of freedom (6-DOF) Stanford manipulator consisting of 3-DOF mechanical arm and 3-DOF spherical wrist. By using Denavit-Hartenberg (DH) method, the Euler-Lagrange equations of motion of mechanical arm subsystem and spherical wrist subsystem are established respectively. A new version of backstepping based adaptive sliding mode controller is proposed for trajectory tracking of each subsystem. In order to grasp an object from one point to another, a special smooth continuous trajectory is planned by inverse kinematics analysis which transforms the position of the end-effector in the task space to the joint position in the joint space. After that, a multi-stage switching control strategy is proposed to achieve trajectory tracking control. Simulation results are provided to demonstrate the performance of the proposed control strategy.

 

 

非线性抛物问题和薛定谔问题有限体积元方法高效数值格式

娄玉芝

 

本文将两网格方法分别运用于求解拟线性抛物问题和线性薛定谔问题。先针对抛物问题提出二阶Crank-Nicolson 两网格有限体积元格式，该格式包含在粗网格空间上求解一个小的原问题，然后在细网格空间上求解一个线性化问题。之后又针对薛定谔问题提出一阶Backward Euler两网格解耦算法，该算法是在粗网格空间上求解原始耦合问题，然后在细网格空间上求解包含了两个独立Poisson问题的解耦系统。我们进一步证明了两个格式相应的误差估计，最后数值算例验证了理论结果，并表明两网格方法在求解非线性问题和耦合问题时，比标准有限体积元方法，在保持精度的条件下具有更高的计算效率。

 

 

Prescribed performance control for uncertain flexible-joint robotic manipulators driven by DC motors

马开法

 

This paper is devoted to the prescribed performance control for a class of flexible-joint robotic manipulators driven by DC motors. Remarkably, certain transient performances are given aforehand which are jointly considered with some steady ones and hence result into the incapability of traditional control methods on this topic. Moreover, more serious uncertainties are allowed than those of the related literature due to the consideration of the dynamics of joint and motor which introduce essential obstacles in the control design. For this, by using the vectorial backstepping method and the constructive method based on funnel set, a novel prescribed performance control framework is established, and in turn one time-varying controller is explicitly designed which guarantee all the closed-loop system signals are bounded, and particularly, the system output tracks the given reference signal with prescribed accuracy and regulation time. A simulation example is provided to validate the effectiveness of the proposed theoretical results.

 

 

Unconditionally energy stable, splitting schemes for magneto-hydrodynamic equations

王琨

 

   In this paper, we propose first-order and second-order linear, unconditionally energy stable, splitting schemes for solving the Magneto-hydrodynamics (MHD) system. These schemes are based on the projection method for Navier-Stokes equations and implicit-explicit treatments for nonlinear coupling terms. We transform a double saddle points problem into a set of elliptic type problems to solve the MHD system. Our schemes are efficient, easy to implement, and stable.  We further prove that time semi-discrete schemes and fully discrete schemes are unconditionally energy stable. Various numerical experiments, including Hartmann flow and lid driven cavity problems, are implemented to demonstrate the stability and the accuracy of our schemes.

 

 

Controllability of neighborhood corona product networks

于越

 

In this paper, a composite network, which is formed by the neighborhood corona product of two factor networks, is considered. A necessary and sufficient condition to verify the controllability of the network is established through some properties of the factor networks. In addition, some sufficient or necessary conditions are proposed to verify the network controllability more easily. Finally, several examples are presented to demonstrate the effectiveness of our methods.

 

 

一类奇异的Monge-Ampère方程Dirichlet问题解的最优全局渐近行为

张博

 

This paper mainly studies the existence and the optimal global asymptotic behavior of the unique classical convex solution to a singular Dirichlet problem for the Monge-Ampère equation  where  is bounded and strictly convex smooth domain in is a positive and decreasing function in  is a positive function in , but may vanish or blow up on the boundary. Our method is based on constructing the suitable sub- and sup-solutions. When the parameters on b tend to the corresponding critical values, we reveal the boundary behavior of the such solution.

 

 

 

 

 

 

 

子群完备码

张星

 

若有限群的子群是的某个Cayley图的完备码, 则称为群的子群完备码。完备码(也称作有效控制集或独立的完备控制集)是图论研究中的一个重要课题, 并且与编码理论、群论有很强的联系。其中Cayley图中的完备码更是在通信网络的设计和分析、资源的优化配置等方面起着至关重要的作用。

我们首先给出了一些有限群的子群可作为Cayley图完备码的条件, 并利用这些条件分别具体找出了广义四元数群、半二面体群以及拟二面体群上Cayley图中的所有子群完备码。

 

 

PUMA560在随机干扰下的抓取控制

钟鹏

 

本文研究了PUMA560在随机干扰下的抓取控制. 利用动静法和相对运动将环境中的随机振动转化为对力矩的随机干扰并结合D-H方法和拉格朗日方法建立PUMA560的动力学方程. 给定起点(终点), 抓取点和放置点, 利用基于三次多项式的路径规划规划出参考路径. 基于建立的模型, 利用共同李雅普诺夫函数设计随机切换控制器使得机械臂尽可能地按照规划的参考路径抓取物体, 同时保证闭环系统的所有信号依概率有界. 最后仿真结果说明了控制策略的有效性.