Asymptotic Nonlinear Filtering and Large Deviations with Application to Observer Design

An important problem in control theory is the design of observers for nonlinear control systems. By observer we mean a deterministic dynamical system which uses observed information to compute an estimate of the state of the control system in such as way that the error decays to zero. Baras and Krishnaprasad have proposed that an observer design might result from a study of an asymptotic nonlinear filtering problem obtained by adding small noise terms to the equations defining the control system. The purpose of this thesis is to study this asymptotic filtering problem and to develop observer designs based on their idea.