A Class of Robust Stabilization Problems in Nonlinear Control

ECS-9707927 研究了一类参数化非线性系统鲁棒镇定的两个相关问题。 第一个方面与稳定的一个家庭时，参数徘徊在一个标称值的线性近似有一个非平凡的不稳定的不可控部分。 这样的系统被称为经历C-分叉。 建议的研究旨在开发分析工具，系统地研究控制系统的C-分岔点附近的动态行为。 包括在寻求的工具是如何提取出一个低维子系统，其中包含重要的信息，定义相关的等价关系和组行动和方法来研究他们通过其线性化，分类，识别和规范形式的低CO维C-分支，和分类的鲁棒稳定性等规范形式的属性。 第二个方面与参数化的家庭，其中的参数是时间相关的，但在某种程度上，只有部分知识是先验的。 为了简化问题，假设参数变化在时间上分段恒定。 寻求反馈控制律，以鲁棒稳定的家庭。 建议的研究将在非线性控制理论的微分几何方法的框架内进行。 基本工具将来自奇点理论和全局微分拓扑。

ECS-9707927 Dayawansa It is proposed to study two related aspects of the robust stabilization of a parameterized family of nonlinear systems. The first aspect has to do with stabilization of a family when the parameters hover around a nominal value at which the linear approximation has a nontrivial unstable uncontrollable part. Such systems are referred to as undergoing C-bifurcation. Proposed research aims at developing analytical tools to systematically study dynamical behavior of a control system near a C-bifurcation point. Included among the sought after tools are ways to extract out a low dimensional subsystem which contains crucial information, definition of pertinent equivalence relations and group actions and ways to study them via properties of their linearization, classification, recognition and normal forms of low CO-dimensional C-bifurcation, and classification of robust stabilizability properties of such normal forms. The second aspect has to do with parameterized families where the parameters are time dependent, but in a way in which only partial knowledge is available a priori. To simplify matters parameter variation is assumed to be piecewise constant in time. Feedback control laws are sought to robustly stabilize the family. Proposed research will be carried out within the framework of differential geometric methods in nonlinear control theory. Basic tools will come from singularity theory and global differential topology.