| This thesis provides a description of the research work conducted, primarily under the supervision of Prof. Christopher DeMarco of the University of Wisconsin-Madison and Dr. Ilya Kolmanovsky of the Ford Motor Company, in the subject area of stochastic delay differential system observers. There are two related primary bodies of work which will be addressed in this document including the construction of observers having bounded error and associated extensions where one or more system faults are present. This body of work is motivated by distinct problem areas in the construction of tracking observers under unknown system delay dynamics and, as a key problem within that general topic, fault detection. Some aspects of these problems have received much attention over the past decade, but the work to be described here has identified a number of important questions that have received little attention in the literature.; The research topic is motivated by the lack of prior work in the literature, on the tracking of system dynamics having dynamic stochastic delay and by problems in fault detection, with specific emphasis on classes of problems anticipated in the control of automotive vehicle subsystems. The work includes studying the effects of system time delays on the detectability of additive faults. It will be shown that consideration of additive faults is sufficient because it allows a general faults structure which can represent general additive and multiplicative faults. It will be shown that under certain constraints, the detection problem can be solved using a proposed observer scheme. In addition, the concept of fault masking will be introduced in which the dynamics associated with the occurrence of system faults can be masked by system delays. The effects of delay masking the dynamics associated with system faults and the associated effects on the evolution of the system dynamics will be described and addressed using delay approximation methodologies and via a geometric methodology. A residual construction having stochastic parameters is developed, which is sensitive to system faults, and which is shown to provide a polynomial-time computable methodology to identify faults. |
