Study of Observability of Nonlinear Distributed Parameter Systems with Applications to Aeroengines and Chemical Reactions

本课题主要研究非线性分布参数系统的可观测性。它由三个主要部分组成。第一部分研究了如何将无限维系统的可观测性转化为有限维框架，在有限维框架中，利用拓扑等价方法方便了观测器的构建。目的是用常微分方程组描述具有有限维吸引子的非线性分布参数系统的渐近行为。第二部分特别关注航空发动机和化学反应的观测器设计，这两个系统由非线性偏微分方程控制。目的是为航空发动机扰动流的估计以及化学反应状态的估计提供技术方法。最后一部分致力于加强PI研究所的多学科项目。技术限制和/或与当前传感器技术相关的过高成本造成了直接在线测量的所有过程状态变量无法测量的情况。例子包括航空发动机中化学过程的监测和扰动流的估计，这些系统可以用非线性演化方程在数学上描述。必须发展和扩展现有的理论来应对这些挑战。这个项目的重点是发展一种数学方法，这种方法将足以满足状态估计的分析和计算需求。本项目的研究成果将有助于提高航空发动机运行的安全性和效率，推进各种化学反应的控制。

This project focuses on the study of observability of nonlinear distributed parameter systems. It consists of three main parts. The first part studies how to translate the observability of infinite-dimensional systems into the finite-dimensional framework from where observer construction is facilitated via topological equivalence approach. The goal is to characterize the asymptotic behaviors of nonlinear distributed parameter systems that have finite-dimensional attractors by a system of ordinary differential equations. The second part pays particular attention to the observer design for aeroengines and chemical reactions, whose systems are governed by nonlinear partial differential equations. The goal is to provide technical methods for the estimation of disturbed flows in aeroengines as well as the estimation of the states of chemical reactions. The last part is devoted to enhancement of the multidisciplinary program at PI's institute.Technical limitations and/or prohibitively high costs associated with current sensor technology create a situation where all process state variables for direct on-line measurements are not able to be measured. Examples include the monitoring of chemical processes and the estimation of disturbed flows in aeroengines, systems which can mathematically be described by nonlinear evolution equations. Existing theories must be developed and expended to meet these challenges. This project focuses on the development of a mathematical methodology that will be adequate for the analytical and computational needs of state estimations. The research outcome of this project will contribute to the improvement of the safety and efficiency of aeroengine operations and the advancement of the control of various chemical reactions.