Receding horizon H∞ control for discrete-time Markovian jump linear systems

Receding horizon H∞ control scheme which can deal with both the H∞ disturbance attenuation and mean square stability is proposed for a class of discrete-time Markovian jump linear systems when minimizing a given quadratic performance criteria. First, a control law is established for jump systems based on pontryagin’s minimum principle and it can be constructed through numerical solution of iterative equations. The aim of this control strategy is to obtain an optimal control which can minimize the cost function under the worst disturbance at every sampling time. Due to the difficulty of the assurance of stability, then the above mentioned approach is improved by determining terminal weighting matrix which satisfies cost monotonicity condition. The control move which is calculated by using this type of terminal weighting matrix as boundary condition naturally guarantees the mean square stability of the closed-loop system. A sufficient condition for the existence of the terminal weighting matrix is presented in linear matrix inequality (LMI) form which can be solved efficiently by available software toolbox. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

Vegetation effects on mean daily maximum and minimum surface air temperatures over China

Changes in the daily maximum (Tmax) and minimum (Tmin) surface air temperatures and the associated temperature extremes have severe consequences on human society and the natural environment. In this study, we assess vegetation effects on mean Tmax and Tmin over China by computing a vegetation feedback parameter using the satellite-sensed Normalized Difference Vegetation Index (NDVI) and observed temperatures for the period 1982–2002. In all seasons, vegetation exerts a much stronger forcing on Tmax than on Tmin, and thus has a substantial effect on the diurnal temperature range (DTR) over China. Significant positive feedbacks on Tmax and the DTR occupy many areas of China with the feedback parameters exceeding 1°C (0.1 NDVI)–1, while significant negative effects only appear over the summertime climatic and ecological transition zone of northern China and some other isolated areas. Also, the vegetation feedbacks are found to vary with season. In areas where significant feedbacks occur, vegetation contributes to typically 10%–30% of the total variances in Tmax, Tmin, and the DTR. These findings suggest that vegetation memory offers the potential for improving monthly-to-seasonal forecasting of Tmax and Tmin, and the associated temperature extremes over China. Meanwhile, the limitations and uncertainties of the study should be recognized.     

关于可逆半群的局部化

本文讨论可逆半群S在幂等元半格E上的局部化的存在和唯一,然后讨论其与S的最小群同余之间的关系。     

最小费用流问题的多重最优解

本文提出了可调圈的概念，并力图对最小费用流问题的多重最优解进行一些探讨。     

对单变量三次函数求极值的一种简便方法

本文给出单变量三次函数是否存在极值的一种简便判别法，由稳定点个数来判别单变量三次函数是否存在极值，并求其极大（小）值。     

熵、巨势与开放的近平衡系统热力学第二定律的两种表现形式

从分析局域平衡理论框架内封闭热力学系统之熵产生与特性函数变率的关系入手，阐明了非平衡态的热力学特征，即非负耗散强度及非平衡线性区向最小耗散态演化的趋势，实际上是分别体现在热力学势的一阶及二阶变率层次上的状态演化方向。同时，提出了以巨势为基础的开放非平衡系热力学第二定律的表述形式，论证了在近平衡区与最小熵产生原理的等价关系。     

任意无向图的最小R边连通扩充

研究了以最少边集扩充一个任意无向图为R边连通图这一优化问题。给出了一个复杂度为O(|V|~5)的算法。利用该算法可最优地将所研究图形中任意两点达到所要求的边连通度。它发展了K边连通最优扩充的研究,从而使图的边连通扩充的研究在应用于网络结线的可靠性设计方面更具有实际意义。     

全局收敛的多输入多输出最小方差自校正调节器

提出了可以控制具有不同传输延时的多输入多输出系统的自校正调节器。分析了该调节器的稳定性和收敛性。证明了该调节器具有全局收敛特性,即以概率1输入输出采样均方有界,条件均方输出取得极小值。     

一个估计的非负最优性

考虑多元线性模型Y=X_1BX'_I+Uε,Eε=0.假设ε=ε,Eεε’=I∑,Covεε’=2(I∑)(I∑).∑~*是∑的一定意义下的最小二乘估计,C≠0是非负定阵,本文给出了tr(C∑~*)是tr(C∑)的一致最小方差非负二次无偏估计的充要条件。     

加速寿命试验Bayes方法的一个注记

本文在失效分布未知条件下,使用Bayes方法在先验分布取为负对数Gamma分布的情况下,首先给出各种应力水平下平均失效率的估计,然后利用这些估计值给出加速寿命模型,从而得到正常应力下的平均失效率估计。本文最后通过一个数值例子,详细地叙述了使用这种方法的全过程。