Observer Construction for Systems of Differential Algebraic Equations using Completions

This dissertation presents the results from researching observer construction for systems of differential algebraic equations using completions. Physical systems of interest in control theory are sometimes described by ordinary differential equations (ODEs) and algebraic equations, forming a system of differential algebraic equations (DAEs). Challenges from solving a system of DAEs come from the first derivative of its state vector having a singular coeffcient matrix and from possibly implicit algebraic constraints defining its solution manifold. These challenges exist for observing a system of DAEs as well, leading to processes that require the system to meet certain assumptions.;Our approach of pairing a completion of a system of DAEs with observers for systems of ODEs has been successful in estimating the states of linear time-invariant and linear time-varying example systems of DAEs without requiring any structural assumptions about the systems. The material on completions and two of the observers is review, but observing a system of DAEs by observing a completion is a new approach. Two other observers included in this dissertation result from our research and take advantage of the constraints characterizing the solution manifold of the system of DAEs. In particular, our maximally reduced observer is shown experimentally to be the preferred observer when compared with traditional full-order and reduced-order observers. With the potential for our approach to be extended to nonlinear systems of DAEs, constructing observers for systems of DAEs using completions looks to be a general approach applicable to both linear and nonlinear systems.