基于T-S模型的Lurie混沌系统的模糊控制

针对Lurie混沌控制系统,进行了T-S模糊建模和模糊控制器设计,从而实现了Lurie混沌系统的稳定.在用T-S模糊模型精确重构Lurie系统结构的基础上,利用反馈同步思想,基于并行分布补偿(PDC)技术,得到了简单且易实现的控制器.仿真结果验证了该控制方法的有效性.     

一类混沌系统的函数矩阵投影同步

研究了一类混沌系统的函数矩阵投影同步问题,基于函数矩阵方法,利用Lyapunov稳定性理论和极点配置理论,设计了两个连续混沌系统之间的同步方案,同时设计了两个离散混沌系统之间的同步方案,实现了驱动系统与动态系统按给定的函数矩阵投影同步,并给出了证明,通过对Lorenz混沌系统,和Henon系统的数值模拟,表明了该方法的有效性.     

整数阶分数阶Rucklidge混沌系统的自适应滑模同步

基于分数阶自适应滑模同步理论研究不确定Rucklidge混沌系统的同步,得到了不确定分数阶Rucklidge混沌系统取得自适应滑模同步的充分条件,研究表明:构造适当的控制律与滑模函数,整数阶分数阶不确定Rucklidge系统取得自适应滑模同步.     

一类分数阶超混沌系统修正函数投影同步的滑模控制

对一类具有未知参数的分数阶超混沌系统的修正函数投影同步进行研究.通过设计响应系统的补偿器,进而得到修正函数投影同步的误差系统.基于自适应滑模控制理论和分数阶微分系统的稳定性理论,设计了一种自适应同步的控制方案.通过选取自适应滑模控制器以及参数自适应控制率,最终实现了驱动系统和响应系统修正函数投影同步,并可以对不确定参数进行估计.最后针对结论,以分数阶超混沌L(u|¨)系统为例,利用Adams-Bashfortlh-Moultom算法进行数值仿真,其结果说明了该方法的有效性和可行性.     

异结构离散型混沌系统的延迟同步

以异结构离散型混沌系统为研究对象,设计了一种延迟同步控制器实现了离散型Henon混沌系统和Ikeda混沌系统之间的同步控制.根据稳定性定理,确定了延迟同步控制器的结构以及系统状态变量之间的误差方程.设计的延迟同步控制器对于不同的离散型混沌系统具有统一的形式,可以实现任意异结构离散型混沌系统之间的延迟同步.数值仿真模拟进一步验证了该控制器的有效性.     

受扰不确定混沌系统的降阶修正函数投影同步

研究了具有不同阶数的受扰不确定混沌系统的降阶修正函数投影同步问题.基于Lyapunov稳定性理论和自适应控制方法,设计了统一的非线性状态反馈控制器和参数更新规则,使得混沌响应系统按照相应的函数尺度因子矩阵和混沌驱动系统的部分状态变量实现同步.方法考虑了实际系统中的模型不确定性和外界扰动,具有较强的实用性和鲁棒性.数值仿真证明了控制方法的有效性.     

Feng混沌系统参数识别及自适应模糊控制器的反步设计

设计了参数观测器,对Feng混沌系统中未知参数进行识别.采用反步控制方法,在存在输入扰动项的情况下,构造模糊自适应控制器控制Feng混沌系统.模糊逻辑系统用来逼近反步控制方法中出现的未知、非线性且结构复杂的函数.和传统的反步控制方法相比,本文采用的控制器结构简单,易于实现.仿真的结果验证了本文控制方法的有效性.     

基于主动滑模控制的混沌系统函数投影同步

研究了一类混沌系统的函数投影同步问题.基于Lyapunov稳定性理论和主动滑模控制方法,设计了主动滑模控制器,实现混沌系统的函数投影同步.数值仿真验证了该控制器的有效性和正确性.     

分数阶二次非线性Sprott混沌系统的滑模同步控制

本文利用滑模控制方法研究了分数阶二次非线性Sprott混沌系统的同步控制问题.根据分数阶微积分的相关理论,得到了系统取得同步的充分性条件,结果表明:选取适当的控制律下,分数阶Sprott主从系统取得滑模混沌同步.     

基于混沌同步化的广义无源性

对一般类型的混沌系统,提出了一个新的基于同步化的无源性.以Liapunov理论和线性矩阵不等式(LMI)逼近为基础.基于无源性的控制器,不仅要求其同步误差系统无源,同时要求其渐近稳定.解线性矩阵不等式表示的凸最优化问题,可以求得所建议的控制器.对Genesio-Tesi混沌系统和Qi混沌系统的仿真计算,证明所建议格式的有效性.     

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.