Metric Uncertainty and Robust Control of Nonlinear Systems

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9505995 Georgiou The research proposed represents a continuation of our current program in developing theoretical and computational tools for modeling and control of dynamical systems. Our approach relies on the concept of the graph. Model uncertainty is quantified using the gap metric which measures potential graph perturbations, and suitable margins are developed to ascertain performance and robustness of stability for the uncertain system. In our past research, we have developed computational and theoretical tools for robust control of linear systems with an energy-type (L2-norm) performance specification. The use of these tools has been demonstrated via application studies, and related software has become available within a standard commercial package (u-tools). Over the next three years, we propose an intensive program to develop theoretical and computational tools for robust control of nonlinear systems. The robustness will be quantified using suitable gap-like metrics. In particular, we introduce a variety of possible distance measures which may be appropriate in different situations. We propose to compute suitable robustness margins which guarantee robustness of stability and performance. These margins can be tailored to a variety of Lo, L2, global, and semi- local stability and performance requirements. Further, we will develop related tools for robust feedback design under such metric uncertainty. Emphasis will be placed on computational issues and application studies. ***