Mathematical Sciences: Operator and Systems Theory

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This project will study H-infinity control theory. The topics to be emphasized are linear time-invariant finite- dimensional plants, Wiener-Hopf factorization and interpolation for rational matrix functions, distributed parameter systems, and H-infinity optimization for nonlinear systems. Morse theory, operator and function theory are expected to play a central role. The problems to be studied are motivated by the need of controlling engineering systems. This project includes nonlinear cases where the known theory for a narrow band of frequencies does not apply. Computer codes will be developed upon successful understanding of the underlying mathematical theory.