Multi-model DAE Based Observer and Filter Design

不同代数方程（DAE）是一个隐式微分方程，与各种量、它们的变化率、控制项和源项有关。DAEs是描述许多工业和科学过程的自然方式。DAE公式通常比使用显式方程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公式会带来一些技术挑战。最近，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、模型识别和故障检测，可以很自然地视为涉及DAEs的问题。在过去，这主要是对低维线性系统的检验。提出了对大型复杂非线性系统进行研究的方法。特别是，系统与延迟和混合离散连续动力学将被检查。理论和实际，鲁棒，数值算法将开发。要检查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。研究结果将应用于航空航天、化学加工和其他行业。

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.