U.S.- UK Cooperative Research: Robust Control of Dynamical Systems

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This award will support collaborative research in systems engineering between Dr. Tryphon Georghiou, University of Minnesota, and Dr. Malcolm Smith, University of Cambridge, England. The objective of the project is to develop novel theoretical tools and techniques for the analysis and design of control systems. Specifically, the goal of the research is to develop an integrated approach to identification, modeling and control for linear dynamical systems. The approach is based on the notion of a graph of dynamical systems. Uncertainty, perturbations and modeling error are measured by the gap metric. The gap metric is a notion of distance between systems suitable for use in the context of robust stabiliza- tion and control. This notion of distance is independent of any particular representation (e.g. state-space, transfer function, or any special system of coordinates) and applies equally well to the most general class of infinite-dimensional distributed parameter systems (e.g. flexible structures). The proposed research will focus on quantitative estimates of modeling/identification error/uncertainty measured by the gap metric and their effect on stability/performance of feedback systems. The immediate impact of this research is expected to be in the development of new control design methodologies. The development of the gap metric, as a tool for analysis and design of robust control systems, has been the main theme of recent work of the two investigators. The project will benefit from the complementary expertise of the investigators in control theory and their history of past successful collaboration.