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

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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.