Rationalized Haar approach for nonlinear constrained optimal control problems

This paper presents a numerical method for solving nonlinear optimal control problems including state and control inequality constraints. The method is based upon rationalized Haar functions. The differential and integral expressions which arise in the system dynamics, the performance index and the boundary conditions are converted into some algebraic equations which can be solved for the unknown coefficients. Illustrative examples are included to demonstrate the validity and applicability of the technique.     

A control parametrization algorithm for optimal control problems involving linear systems and linear 1

Computational schemes based on control parametrization techniques are known to be very efficient for solving optimal control problems. However, the convergence result is only available for the case in which the dynamic system is linear and without the terminal equality and inequality constraints. This paper is to improve this convergence result by allowing the presence of the linear terminal inequality. For illustration, an example arising in the study of optimally one-sided heating of a metal slab in a furnace is considered.     

Sharp bounds for harmonic numbers

In the paper, we collect some inequalities and establish a sharp double inequality for bounding the n-th harmonic number.     

两个著名不等式的加强式及其反向不等式

从一对离散型双向不等式出发，推广到相应的积分型双向不等式，然后通过代换，获得积分型Holder不等式和积分型H．Minkowski不等式的加强式及其反向不等式，从而拓广其应用范围。     

基于观测器的模糊Delta算子系统的控制器设计

对于非线性模糊系统控制器和观测器的分析和设计,提出一种统一方法。利用Delta域离散T—S模糊模型对非线性系统建模,并基于李雅普诺夫稳定性理论给出模糊状态反馈控制器和观测器的设计策略,将所得结果归结为求解一组线性矩阵不等式。同时结论表明:分离性原理对Delta算子T—S模糊系统仍然成立。所得结果可将现有关于连续和离散T—S模糊系统的相关结论统一于Delta算子框架内。     

An inequality for distances between 2n points and the Aleksandrov-Rassias problem

In this paper, we introduce an inequality for distances between every two points among the given 2n points and apply this inequality to a partial solution of the Aleksandrov-Rassias problem, which was first posed by Th.M. Rassias.     

A TRUST—REGION ALGORITHM FOR NONLINEAR INEQUALITY CONSTRAINED OPTIMIZATION

This paper presents a new trust-region algorithm for n-dimension nonlinear optimiza-tion subject to m nonlinear inequality constraints.Equivalent KKT conditions are derived,which is the basis for constructing the new algorithm.Global convergence of the algorithun to a first-order KKT point is eatablished under mild conditions on the trial steps.local quadratic convergence theorem is provcd for nondegenerate minimizer point.Numerical expcriment is prcsented to show the effectiveness of our approach.     

气体动力学压差方程一类波的相互作用

该文利用一个分析不等式,得到了气体动力学压差方程前向激波追赶前向激波相互作用的结果为后向激波与前向激波相离     

Elliptic Integral Inequalities, with Applications

The authors study monotoneity and convexity of certain combinations of elliptic integrals and obtain sharp inequalities for them. Applications are provided. November 23, 1994. Date revised: February 5, 1997.     

C-代数上的Fourier变换和C-代数上的Vinogradov不等式

本文给出了C-代数上的Fourier变换，从而推广了经典数论上Fourier变换和任意有限Abel群的Fourier变换．进一步应用这个Fourier变换，给出了C-代数上的Vinogradov不等式．