Horton, Kirk Gerritt. Fault Detection and Model Identification in Linear Dynamical Systems. (Under the direction of Dr. Stephen La Vern Campbell.) Linear dynamical systems, Ex'+Fx=f(t), in which E is singular, are useful in a wide variety of applications. Because of this wide spread applicability, much research has been done recently to develop theory for the design of linear dynamical systems. A key aspect of system design is fault detection and isolation (FDI). One avenue of FDI is via the multi-model approach, in which the parameters of the nominal, unfailed model of the system are known, as well as the parameters of one or more fault models. The design goal is to obtain an indicator for when a fault has occurred, and, when more than one type is possible, which type of fault it is. A choice that must be made in the system design is how to model noise. One way is as a bounded energy signal. This approach places very few restrictions on the types of noisy systems which can be addressed, requiring no complex modeling requirement. This thesis applies the multi-model approach to FDI in linear dynamical systems, modeling noise as bounded energy signals. A complete algorithm is developed, requiring very little on-line computation, with which nearly perfect fault detection and isolation over a finite horizon is attained. The algorithm applies techniques to convert complex system relationships into necessary and sufficient conditions for the solutions to optimal control problems. The first such problem provides the fault indicator via the minimum energy detection signal, while the second problem provides for fault isolation via the separating hyperplane. The algorithm is implemented and tested on a suite of examples in commercial optimization software. The algorithm is shownto have promise in nonlinear problems, time varying problems, and certain types of linear problems for which existing theory is not suitable.
