Auxiliary Signal Design for Fault Detection for Nonlinear Systems: Direct Approach

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Title: Auxiliary Signal Design for Fault Detection for Nonlinear Systems: Direct Approach
Author: Andjelkovic, Ivan V.
Advisors: Negash Medhin, Committee Member
Pierre A. Gremaud, Committee Member
Stephen L. Campbell, Committee Chair
Ralph Smith, Committee Member
Abstract: The main task of active fault detection is to design an auxiliary signal which acting on the system will reveal to the observer a potential fault of the system. There are numerous results that implement techniques of optimal control to calculate an auxiliary signal. However, the techniques and methods are almost exclusively designed for linear systems, while nonlinear systems are treated through linearization. In this thesis, we are providing a novel way of directly approaching nonlinear systems. We will start with a brief overview of the areas of the fault detection, optimal control, basic terminology and principles of active fault detection and previous research. Then we will present the novel p-norm approach enabling us to solve nonlinear problems directly using optimization. We will develop a direct optimization formulation for active fault detection for linear and nonlinear systems with additive uncertainty. We will present some test examples and point out the advantages and disadvantages of our new p-norm approach. Several illustrative examples will be presented and analyzed for a deeper understanding of underlying problems involved with nonlinear systems. We are hoping that this thesis will give guidelines for future users and researchers of how to approach active fault detection on nonlinear systems. Linear systems with model uncertainty have already been analyzed using the Riccati equations. Here we will develop a direct optimization formulation. After some test examples, we will solve several types of problems that cannot be solved using the Riccati approach, namely problems that contain additional constraints (soft or hard) on states of the system or on auxiliary signals. The quality of an auxiliary signal is usually measured by some cost function. We will examine the influence of several cost functions on our auxiliary signal design.
Date: 2008-05-06
Degree: PhD
Discipline: Applied Mathematics

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