August 2, 19959417004 Datta The research proposed here addresses fundamental problems in three distinct areas: a)Robust Control with an emphasis on parametric uncertainty b)Adaptive Control with an emphasis on robustness and performance issues and c)Robust Adaptive Control with the thrust being the development of new quantitative analysis and design methods exploiting the recent explosion of results obtained using Kharitonov's Theorem and its extensions. First, we intend to develop "best case" results involving the parametric stability margin, Hoo stability margin (norm), gain and phase margins over a parametrized set of transfer functions, such as an interval plant. These robustness results in the area of Robust Parametric Stability, would then be used for non- conservatively quantifying the robustness of adaptive control schemes. The second objective is to develop extremal parametric results involving the H2 and L1 norms which, we believe, will play an important role in studying adaptive system performance. The third objective is to address some important open problems in each of the areas of adaptive control and robust parametric stability. The objectives mentioned above are motivated from our prior research which has not only enabled us to identify some of the outstanding unresolved problems in the areas of adaptive control and robust parametric stability, but has also highlighted the need for inter-twined research efforts in these two traditionally very diverse fields. None of the existing theory in either of these fields can solve the problems related to this proposal in a practical or satisfactory manner. However, successful resolution of these problems is imperative from both a theoretical and a practical point of view. Indeed, practitioners of both robust and adaptive control stand to benefit a lot from the "non- conservative" parametric L1 and Hoo robustness results that we seek to develop. ***
