非线性控制系统的层次化与机械化

Hierarchy Structure and Mechanization of Nonlinear Control Systems──An exploration on new developing direction

中文关键词  Wbitney拓扑  正则型  中心流形  代数族  纤维丛

英文关键词  Whitney topology  normal form  centre manifold  algebraic variety  fibber bundle

中文摘要

      本文首先对非线性系统的几何理论作一回顾，指出它的进展与目前的瓶颈所在，然后提出一个大胆的设想：通过对非线性控制系统的层次化结构分解与机械化的计算机实现，发展现有的非线性系统的几何理论，使非线性控制系统的模型有穷参数化，从而为控制设计及工程应用提供一个便于用计算机实现的基本框架，为实现理论上的突破，本文提出三个新的理论工具：微分动力学，微分拓朴学与代数拓扑，代数几何，然后，对每种工具在新模型框架下所起的作用及所要解决的问题进行粗线条的勾画，并详细说明目前的进展与下一步的期望。

英文摘要

      First of all，this paper gives a review for the geometric theory of nonlinear control systems，shows its advance and points out the bottle-neck for further development. Then an ambitious proposal is presented. Turn over a new leaf for geometric theory of nonlinear control systems via hierarchy-structure decomposition and mechanized computer realization. That consists of finite-parameter-modelling of nonlinear control systems and providing a frame，which is convenient for computer realization of the control design and engineering applications. To realize such a break-through，three new tools are suggested: differential dynamics，differential topology and algebraic topology，and algebraic geometry. In the following the rules played by different tools for solving different problems are sketched. Current advance and further expectation are described in detail.