Mathematical Sciences: Differential Geometric and Real Analytic Methods in NonLinear Control Theory

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Research will be carried out on nonlinear control theory, continuing the Principal Investigator's previous work in this area on a broad class of problems on local and global controllability, observability, minimal realizations, applications to robotics, optimal control and feedback stabilization. The methods used will be those commonly known as "differential geometric control theory," the theory of real analytic maps and their associated stratifications, and the theory of real analytic desingularization. Specifically, efforts will be made to solve a number of open problems in the areas of optimal control, controllability, and realization theory of both continuous time and sampled continuous time systems, while pursuing the development of the necessary mathematical tools -- especially on the theory of real analytic stratifications.