基于自适应模糊控制方法的四翼混沌系统有限时间同步

研究了一类带有未知外部摄动的四翼混沌主从系统的有限时间同步控制问题.首先,基于自适应模糊控制方法,对四翼混沌系统的不确定项进行了处理.其次,基于Lyapunov有限时间稳定性准则,设计了一种有限时间同步控制器,使得主系统与从系统能在有限时间内实现状态同步.最后,通过数值仿真,检验了该方法的有效性和鲁棒性.     

广义不确定周期时变系统的鲁棒非脆弱控制

研究了状态矩阵具有不确定性的广义周期时变系统的鲁棒非脆弱控制问题.利用线性矩阵不等式(LMI)方法,分别对控制器增益具有加法式摄动和乘法式摄动两种情形加以讨论,而非脆弱控制器的设计可以通过求解一组线性矩阵不等式得到.最后,数值例子说明了所给方法的有效性.     

一类随机非线性系统的全局有限时间状态反馈镇定

研究一类连续但非光滑的随机非线性系统的全局有限时间状态反馈镇定控制问题.通过增加幂次积分器技术和四次Lyapunov函数的构造,系统地给出了系统状态反馈有限时间镇定控制器的设计方法.基于引入的随机非线性系统有限时间稳定的判定准则,可以证明闭环系统的有限时间稳定性.仿真结果进一步验证了所设计控制器的有效性.     

一类高阶非线性系统停息时间可调的有限时间镇定

研究了一类高阶非线性系统停息时间可调的有限时间稳定性分析与控制器设计问题.利用有限时间Lyapunov定理的反步构造法,设计状态反馈有限时间控制器,并实现停息时间的适当调整.     

基于圆判据的一种LMI绝对镇定方法

针对非线性Lur'e系统,提出了一种输出反馈控制器综合方法。对于系统在无摄动及线性部分存在乘性范数摄动的情况,分别设计了保证闭环系统绝对稳定的动态输出反馈控制器。由圆判据出发,通过把绝对稳定性问题等价地转化成H∞控制问题,得到了一组由线性矩阵不等式(LMI)表达的控制器存在的充分性条件。     

带有Markovian跳变参数和执行器故障的切换LPV系统有限时间可靠控制

研究了一类带有Markovian跳变参数和执行器故障的切换LPV系统的有限时间可靠控制问题.考虑的子系统都是参变子系统,更具有一般性.同时把此类系统要求转移概率完全已知的条件放宽到了转移概率部分未知的情形,具有更少的保守性.首先,给出了保证带有Markovian跳变参数的切换LPV系统有限时间稳定的充分条件.然后,提出了带有Markovian跳变参数和执行器故障的切换LPV系统的有限时间可靠控制问题,并设计了一个有限时间可靠控制器.最后,数值算例说明了所得结果的有效性.     

非线性系统有限时间受限控制

任何实际的系统均受到不同形式的限制,例如状态受限、输入饱和等.还有一种限制是传感器或执行机构数量的不足.文章主要研究了传感器和执行机构数量不足情况下的非线性系统有限时间控制问题.针对这类间题获得了有限时间镇定控制的设计方法,并讨论了相应的控制器的实施问题.通过对某Lorenz混沌系统的仿真应用模拟,验证了所提出设计方法的可行有效.     

一类自治细胞神经网络的全局有限时间同步控制

通过利用广义线性状态误差反馈控制器,研究了一类自治细胞神经网络模型的全局有限时间同步控制问题.把一种具有简单结构的广义线性状态误差反馈控制器引入到控制策略中,得到了模型有限时间同步的易于验证的数学判据.     

基于自适应控制的四元数时滞神经网络的有限时间同步

文章主要研究了自适应控制下四元数时滞神经网络的有限时间完全同步,通过设计一组有效新颖的自适应控制器,使得主从系统实现有限时间同步,并计算出停息时间的理论估计.利用Lyapunov函数方法和不等式技巧,给出了四元数时滞神经网络主从系统有限时间同步的充分条件.最后,通过数值仿真验证了所得理论结果的有效性.     

一类具有饱和因子的奇异时滞系统的鲁棒保性能控制

研究了具有饱和因子的非线性奇异时滞系统的鲁棒保性能控制问题.目的是设计一个鲁棒控制器和保成本控制器,通过线性矩阵不等式方法(LMI)得出了鲁棒控制器和保性能控制器存在的充分条件.当这些LMI方法是可解时,分别给出了鲁棒控制器和保性能控制器的解析表达式.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.