A Class of Robust Stabilization Problems in Nonlinear Control

ECS-9707927 Daawansa建议研究一类参数化非线性系统的鲁棒镇定的两个相关方面。第一个方面涉及当参数在标称值附近徘徊时的族的稳定性，在该标称值处，线性近似具有非平凡的不稳定的不可控部分。这样的系统被称为正在经历C-分叉。所提出的研究旨在开发分析工具来系统地研究控制系统在C分叉点附近的动态行为。其中包括提取包含关键信息的低维子系统的方法，相关等价关系和群作用的定义，以及通过它们的线性化性质、分类、识别和低余维C-分叉的标准型来研究它们的方法，以及这些标准型的鲁棒可镇定性质的分类。第二个方面与参数依赖于时间的参数化族有关，但在这种情况下，先验知识只有部分可用。为了简化问题，假设参数变化在时间上是分段不变的。寻求反馈控制律来有力地稳定家庭。拟议的研究将在非线性控制理论中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整体微分拓扑学。

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.