The use of adaptive and learing strategies in engineering systems is important for several reasons including increased robustness against changes in operating conditions and errors in data and modeling, reduced need for explicit programming, and improved performance over time. However, although such strategies have been widely used and studied, certain basic questions such as "What are optimal strategies for adaptation?" and "How much data is required?" remain largely unanswered. Therefore, the design of adaptive and learning systems is generally done in an ad hoc manner with little experience gained from on e application to the next. furthermore, very few performance guarantees can be provided for the algorithms used. The goal of this research is to contribute to the theoretical foundations of adaptive and learning systems. Some particular topics to be pursued include the analysis of estimation and adaptive control algorithms under arbitrary disturbances, the study of fundamental limitations in system identification, and understanding the role of prior uncertainty and feedback in determining system performance. The primary goal is to obtain results on the fundamental capabilities and limitations of adaptive and learning systems in order to allow more principled design and analysis of such systems.
