一类非线性动态系统的混合H2/H∞模糊输出反馈跟踪控制

讨论一类非线性动态系统的混合H2/H∞模糊输出反馈跟踪控制问题。首先利用T-S模糊模型对系统进行建模,然后设计基于观测器的控制器,使跟踪误差尽可能的小,并且对于任何有界参考输入,满足给定的H∞跟踪性能,以及在满足给定的H∞跟踪性能下,达到H2次优控制性能,最后将观测器与控制器的设计问题转化为EVP(特征值问题)。     

A class of two-dimensional rational maps with self-excited and hidden attractors

This paper studies a new class of two-dimensional rational maps exhibiting self-excited and hidden attractors. The mathematical model of these maps is firstly formulated by introducing a rational term. The analysis of existence and stability of the fixed points in these maps suggests that there are four types of fixed points, i.e., no fixed point, one single fixed point, two fixed points and a line of fixed points. To investigate the complex dynamics of these rational maps with different types of fixed points, numerical analysis tools, such as time histories, phase portraits, basins of attraction, Lyapunov exponent spectrum, Lyapunov (Kaplan—Yorke) dimension and bifurcation diagrams, are employed. Our extensive numerical simulations identify both self-excited and hidden attractors, which were rarely reported in the literature. Therefore, the multi-stability of these maps, especially the hidden one, is further explored in the present work.     

陕北地区黄土节理对公路边坡稳定性的影响

黄土节理主要分为原生节理、构造节理、风化节理和卸荷节理。陕北地区主要发育原生节理和构造节理,原生节理多分布在马兰黄土中,较密集,延伸长;构造节理多分布在离石黄土中,方向性强,区域性强。节理对边坡稳定性的影响因产状不同而不同。与边坡走向一致的顺坡斜节理对边坡稳定性影响较大,垂直节理影响较小;走向与边坡走向垂直和斜交的节理对边坡稳定性影响较小。多组节理在平面内可组成层面棋盘格式和“X”格式;在空间内可组成板状结构体、楔椎状结构体和柱状结构体。不同形状的结构体对边坡产生不同影响。最后,针对对边坡稳定性影响最大的斜节理,讨论了沿构造(斜)节理面产生边坡土体滑落的可能性的核算方法。