Control and stabilization of the Korteweg-de Vries equation: recent progresses

The study of the control and stabilization of the KdV equation began with the work of Russell and Zhang in late 1980s. Both exact control and stabilization problems have been intensively studied since then and significant progresses have been made due to many people's hard work and contributions. In this article, the authors intend to give an overall review of the results obtained so far in the study but with an emphasis on its recent progresses. A list of open problems is also provided for further investigation.     

二阶积-微分方程奇异边值问题解的存在性

讨论了一类二阶积 微分方程两点边值问题解的存在性。该问题以四阶微分方程两点边值问题为特例。首先在不假设非线性项单调,并允许其有奇性的情况下,利用上下解方法与Schauder不动点定理,获得了二阶Fredholm型积 微分方程两点边值问题解的存在性结果,然后把该结果应用于两端简单支撑的弹性梁的平衡状态模型—四阶微分方程边值问题。     

Decay rates of the hyperbolic equation in an exterior domain with half-linear and nonlinear boundary dissipations

This paper considers the energy decay of the wave equation with variable coefficients in an exterior domain. The damping is put on partly the boundary and partly on the interior of the domain. The energy decay results are established by Riemannian geometry method.     

On a boundary value problem for a Sturm-Liouville type differential inclusion

<正> This paper proves a Filippov type existence theorem for solutions of a boundary valueproblem for a Sturm-Liouville type differential inclusion defined by a nonconvex set-valued map.Themethod consists in application of the contraction principle in the space of selections of the set-valuedmap instead of the space of solutions.     

基于频心法的STAP非均匀检测器

针对杂波谱移动非均匀和功率非均匀现象,提出了"频心"法非均匀检测器。该检测器利用杂波谱移动非均匀和功率非均匀环境下杂波散射中心频率和能量随距离变化这一特点进行非均匀样本选取。仿真结果证明这种非均匀检测器在杂波谱移动非均匀和功率非均匀环境下具有较好的非均匀检测性能。     

New design and analysis of finite difference domain decomposition algorithm for the two-dimensional heat equation

<正> It is presented in this paper that the new design and its analysis of finite difference domaindecomposition algorithms for the two-dimensional heat equation,and the numerical results have shownthe stability and accuracy of the algorithms,where Saul'yev asymmetric schemes have been used atthe interface points.The Algorithm Ⅱ in this paper has further extended those developed by Dawsonand the others,Zhang and Shen.     

基于PLS-结构方程的顾客满意度评价方法

传统结构方程模型虽然在分析中既能处理测量误差．又可描述潜变量之间的结构关系、但是，在求解结构方程模型的过程中严格依赖协方差矩阵，并且假设测量变量服从正态分布，由于顾客满意的频数分布常常为非正态分布，从而极大限制了该方法在顾客满意度研究方面的应用．本文研究基于PLS的结构方程模型，有效解决了在构造客户满意度模型中所遇到的变量非正态问题．并以肛结构方程原理为支撑，对商品房顾客满意度问题进行了应用研究．     

面向复杂决策问题的结构计算方法研究

决策问题的复杂性与决策问题的结构化程度是高度相关的,对于决策问题复杂性的研究,主要体现在对策问题结构化的研究上。借鉴复杂系统分层递阶结构的特点,对复杂决策问题的层次结构进行形式化定义,描述了复杂决策问题的结构集成,提出问题结构集成的关键在于支配决策单元的相对权重的获得,运用梯度向量法对复杂决策问题进行层次结构分析,并结合算例验证了该方法的有效性。     

有限理性下的演化博弈与合作机制研究

指出了以Nash为代表的经典博弈论及其纳什均衡解在完全理性假设下的理论缺陷,从而引入有限理性下的演化博弈论.介绍了演化博弈论中策略进化的思想,提出有限理性的实质是怎么去学习,进而探讨了演化博弈中的各种学习模型.介绍了基于个体的学习模型和网络上的演化博弈研究进展;提出了用演化博弈去解释现实复杂网络的设想;分析了网络结构和博弈策略的互演化思想.讨论了演化博弈框架下合作的进化及合作机制的研究进展.最后,对演化博弈今后的发展趋势和研究方向给出了评述.     

基于边界特征点提取的约束Delaunay三角剖分算法

在地形表达上不规则三角网应用广泛,实际中用到最多的也是Delaunay三角网剖分算法。针对约束数据域下的Delaunay三角剖分通常不满足DT特性的问题进行了阐述,分析了已有的三种引入附加点的算法,算法主要从几何的角度考虑如何减少附加点的数量,而加入附加点的最终目的在于获得更加真实的地形,因而提出了基于边界特征点提取的约束Delaunay三角剖分算法,算法实质就是在加入特征约束之前提取能够满足可以真实再现地形的所有特征点作为新的特征约束,省去附加点的概念,应用现有的Delaunay三角剖分算法进行构网,保证构建后的地形仍具真实感。     

Finite element approximation for a class of parameter estimation problems

This paper investigates the finite element approximation of a class of parameter estimation problems which is the form of performance as the optimal control problems governed by bilinear parabolic equations,where the state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions.The authors derive some a priori error estimates for both the control and state approximations.Finally,the numerical experiments verify the theoretical results.     

Backstepping approach to the adaptive regulator design for a one-dimensional wave equation with general input harmonic disturbance

This paper considers the parameter estimation and stabilization of an unstable one-dimensional wave equation with matched general harmonic disturbance at the controlled end. The backstepping method for infinite-dimensional system is adopted in the design of the adaptive regulator. It is shown that the resulting closed-loop system is asymptotically stable. Meanwhile, the estimated parameter is shown to be convergent to the unknown parameter as time goes to infinity.     

一类非线性大系统优化问题的逼近算法

针对一类约束函数是变量可分离的非线性大系统优化问题,本文给出一种基于逐次逼近算法的熵函数法,对每一个子问题,该方法可以通过解一个可微的无约束极小值问题,一次性地获得其ε－最优解,避免了序列极小化过程,并且可以通过参数的选承控制解的误差,初步的数值试验表明,对于该类非线性大系统优化问题,本算法有良好的数值表现。     

频域相关器在低轨小卫星中的应用

针对频域相关器在频域上进行直接序列扩频信号的捕获,可以显著地加快捕获速度,缩短捕获时间,在进行直接FFT补零做法的性能分析后,指出直接补零会带来性能的恶化。然后提出了一种新的算法,即把频域相关长度加倍,证明它可以完美地解决频域相关器的FFT长度不匹配的问题,同时与时域相关器相比,仍然大大地降低了计算量,缩短了捕获时间,并给出了在基于数字信号处理器(DSP)实现时频域相关器和时域相关器的计算量比较结果。     

A note on the nestedness property for ordered median problems in tree networks

The nestedness property has become an increasingly important means for devising efficient algorithms for network location problems. There have been attempts to explore the nestedness property of network location problems with some special cases of the convex ordered median objectives. However, there is little research on the nestedness property for those problems with the concave ordered median objectives. This paper constructs a tree network T and shows that the nestedness property cannot hold for the concave ordered median problem, which fills a gap in the research on the nestedness property. Finally, the authors pose an open problem on identifying the nestedness property for the continuous strategic ordered median problem.     

定制生产下的供应链网络竞争均衡问题研究

针对由多个生产商和多个零售商构成的供应链网络,分析其中生产商间生产能力的竞争、零售商间订购量和零售价的竞争问题,建立最大化期望利润的竞争模型.在零售价对随机需求有影响的条件下,证明了如下结论:多生产商和多零售商构成的网络中,零售商间的博弈实际为分别对各品牌产品的博弈,每个博弈中零售商期望利润函数的极大值点存在;由多个供应商和两个零售商组成的供应链网络中,在一定条件下,零售商间存在均衡定价和订货策略,并给出了最优反应函数;如果批发价格是生产数量的函数,即生产商不采用价格歧视策略,在某种条件下生产商间存在均衡生产数量.最后用一个数值算例分析了模型中的几种竞争关系和成员企业期望利润的变化.     

求解Job Shop调度问题的粒子群算法研究

为解决单一粒子群算法求解Job shop调度问题存在的不足,提出一种基于交换序的混合粒子群算法,提高了这类问题的求解质量.在混合粒子群算法中,采用粒子群算法进行大范围全局搜索.根据Job Shop调度问题解的特征,提出基于关键工序的邻域选择方法,并将基于这种方法的禁忌搜索算法作为局部搜索算法,增强了粒子群算法的搜索能力.采用混合粒子群算法对13个难解的benchmark问题进行求解,在较短的时间内,得到的最优解和10次求解的平均值优于并行遗传算法和粒子群算法.由此说明本文所提出的混合粒子群算法是有效的.     

决策结构设计中的通信网络问题研究

为了适应从“平台中心战”到“网络中心战”的转变,研究了决策网结构设计中的网络容量分配和网络代价问题,全面提升了决策过程和决策质量,在自适应决策结构的构造过程中,根据决策员实时通信结构,建立节点间的信息传输时间模型。在满足平均网络延迟时间最小的基础上,通过计算可获得优化的通信网络容量和网络代价。该研究结果为设计优化的决策网络结构提供了保障,对于提高网络利用率、减少网络构造成本等具有较大的应用价值。     

Sample average approximation method for a class of stochastic variational inequality problems

This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu (2008), by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.     

Hierarchical control based on Hopfield network for nonseparable opti mization problems

1 .INTRODUCTIONConsider thefollowing complexsystemthat comprisesNinterconnected subsystems , the mathematicalmodel of theith subsystemisyi=fi(ci,ui,zi)gi(ci,ui,yi) ≥0ui= Hiywhereci, ui, yiandziare theithsubsystemcontrolinput ,interactioninput ,output and disturbance vec-tor respectively,andfiis the mathematics model oftheithsubsystem.It is assumedthat external distur-bancezwhich affects the systemis constant in theconsidered ti me interval of control and hence will beleft out of the syst…