开流形的曲率与拓扑

应用比较几何的方法研究了完备非紧且具有特定曲率条件的黎曼流形，证明了在一定Pinching条件限制下，流形具有有限拓扑型或者微分同胚于R^n。     

基于微分同胚变换的故障重构算法

针对一类含有未知输入扰动的不确定非线性系统提出一种鲁棒故障重构方案. 采用全局微分同胚变换, 将非线性系统变换为二个子系统, 使得其中一子系统不受故障影响, 状态部分可观, 另一子系统受故障影响但状态完全可观. 利用滑模变结构原理对两个子系统分别设计状态观测器消除扰动对系统的影响后, 再利用等值控制方法实现对故障的重构. 应用案例验证了所提方法的有效性.     

有关流形上Poisson结构的几点讨论

讨论了微分同胚对Poisson流形上Poisson结构的保持，得到了微分同胚所诱导的Poisson括号的一些性质，最后，还得到了有关Poisson流形上的Casimir函数在微分同胚作用下仍然是Casimir函数这一有用的定理。     

欠驱动水面船舶的曲线航迹跟踪控制

针对欠驱动水面船舶的航迹跟踪控制面临着本质非线性、强耦合和无法线性化处理的控制等问题,首先通过对欠驱动水面船舶航迹控制系统的非线性模型.进行全局微分同胚和反馈变换,构造了由2个级联的子系统构成的航迹跟踪误差系统,然后基于反步法的设计原理,运用Lyapunov直接方法对变换后的误差系统设计了航迹跟踪控制律,该控制律可以实...     

基于自适应切空间的MRI图像配准

微分同胚是一种光滑可逆的变换,在MRI图像配准中可以保证图像形变后的拓扑结构保持不变,同时避免出现不合理的物理现象。为了在空间变换中获得更合理的同胚映射,高维空间中数据的非线性结构被考虑,基于流形学习方法提出一种自适应切空间的MRI图像配准算法。首先,把MRI数据构造成对称正定（SPD）的协方差矩阵,然后形成李群;接着,利用样本点邻域的局部切空间来表示李群的几何结构的非线性;接下来,在流形上用自适应邻域选择的方法形成的线性子空间去逼近局部切空间,提高切空间的局部线性化程度,从而最大限度地保留流形的局部非线性结构,得到最优的同胚映射。仿真数据和临床数据的实验结果显示,与传统的非参数微分同胚配准算法相比,该算法在高维稠密形变场上获得更高的拓扑保持度,最终提高图像配准精度。     

Hopfield连续神经网络局部稳定性分析

利用微分几何的方法,将非线性Hopfield神经网络在平衡点附近精确线性化,使之变换成线性系统。通过分析神经网络的n阶李导数,给出并证明了Hopfield神经网络的局部稳定性定理。定理表明,当神经网络满足精确线性化条件时,系统的可控矩阵的非奇异性充分决定了神经网络吸引子的局部稳定范围。     

基于高增益观测技术的高精度感应电机磁链观测器研究

针对感应电机磁链观测的一般方法具有观测精度不高、使用的电机参数多、易受影响等问题,利用非线性微分同胚变换对感应电机强耦合非线性系统进行转化,提出一种基于高增益观测技术的感应电机磁链观测器.该观测器不需要满足状态能观的条件且计算量小,通过调节增益能够达到任意精度误差.对非线性规范型的高增益观测器进行了稳定性分析,证明了收敛性.仿真和实验结果验证了该观测器的高观测精度和所提方法的可行性和有效性.     

Groups of Germs of Analytic Diffeomorphisms in (C2, 0)

Let G be a group of germs of analytic diffeomorphisms in (C², 0). We find some remarkable properties supposing that G is finite, linearizable, abelian, nilpotent, and solvable. In particular, if the group is abelian and has a generic dicritic diffeomorphisms, then the group is a subgroup of a 1-parametric group. In addition, we study the topological behavior of the orbits of a dicritic diffeomorphisms. Last, we find some invariants in order to know when two diffeomorphisms are formally conjugate.     

Automatic segmentation of hippocampal subfields based on multi-atlas image segmentation techniques

The volume of hippocampal subfields is closely related with early diagnosis of Alzheimer＇s disease. Due to the anatomical complexity of hippocampal subfields, automatic segmentation merely on the content of MR images is extremely difficult. We presented a method which combines multi-atlas image segmentation with extreme learning machine based bias detection and correction technique to achieve a fully automatic segmentation of hippocampal subfields. Symmetric diffeomorphic registration driven by symmetric mutual information energy was implemented in atlas registration, which allows multi-modal image registration and accelerates execution time. An exponential function based label fusion strategy was proposed for the normalized similarity measure case in segmentation combination, which yields better combination accuracy. The test results show that this method is effective, especially for the larger subfields with an overlap of more than 80%, which is competitive with the current methods and is of potential clinical significance.     

Geometric Structures of Stable Time-Variant State Feedback Systems

A new technique for considering the stabilizing time-variant state feedback gains is proposed from the viewpoint of information geometry. First, parametrization of the set of all stabilizing time-variant state feedback gains is given. Moreover, a diffeomorphic structure between the set of stabilizing time-variant state feedback gains and the Cartesian product of positive definite matrix and skew symmetric matrix satisfying certain algebraic conditions is constructed. Furthermore, an immersion and some results about the eigenvalue locations of stable state feedback systems are derived.