Multi-model DAE Based Observer and Filter Design

不同的代数方程(DAE)是一种隐式微分方程，它将各种量、它们的变化率以及控制项和源项联系在一起。DAE是描述许多工业和科学过程的自然方式。与使用显式公式相比，DAE公式通常提供更快的模型开发和更准确的建模。然而，在复杂问题上使用DAE公式会带来许多技术挑战。最近的研究表明，控制和系统理论中的一些基本问题，包括观测器设计、模型辨识和故障检测，都可以自然地视为涉及DAE的问题。在过去，这主要是针对低维线性系统进行研究的。建议对大型复杂非线性系统的这些问题进行研究。特别是，具有时滞和混合离散连续动态的系统将被研究。理论和实际的、稳健的、数值算法都将被开发出来。要研究的具体问题包括模型识别、故障检测、观测器设计、系统仿真和故障隔离。该成果将应用于航空航天、化工加工等行业。

A different algebraic equation (DAE) is an implicit differential equation relating various quantities, their rates of changes, and control and source terms. DAEs are the natural way in which to describe many industrial and scientific processes. A DAE formulation often provides the quicker model development and more accurate modeling than when using explicit equations. However, using the DAE formulation on complex problems poses a number of technical challenges. Recently, it has been shown that a number of fundamental problems in control and systems theory including observer design, model identification, and failure detection can be naturally viewed as problems involving DAEs. In the past this has mainly been examined for lower dimensional linear systems. It is proposed to examine these problems for large complex nonlinear systems. In particular, systems with delays and mixed discrete continuous dynamics will be examined. Both theory and practical, robust, numerical algorithms will be developed. Particular questions to be examined include model identification, failure detection, observer design, system simulation, and fault isolation. The results will be applied to applications from the aerospace, chemical processing, and other industries.