Technical Aspects


This conference appears to be at the leading edge of what the organizers hope will be a productive interdisciplinary field.

Of course, the introduction and use of differential-geometric methods in more general PDE theory has long been established. However, the use and role of differential geometric methods toward the solution of any of the modeling, control and optimization problems mentioned in points a), b), c) above, was largely unexplored until very recently. It opens up a highly promising area of research, with unexpected links which have been already made (e.g. the use of covariant differential calculus for Levi-Civita connections associated with the differential, variable coefficient, principal part, elliptic operator, to obtain general Carleman-type estimates for PDE solutions), with many more still to be discovered.

By contrast, the introduction of differential-geometric methods in the study of control problems (such as exact controllability, feedback stabilization, optimization, filtering, etc) for dynamical systems modeled by ordinary differential equations (ODEs) dates as far back as the early '70s. At present, the label "geometric control theory" is reserved to this established branch, whose status is well documented (see e.g. the proceedings of a Symposium "Motion, control, geometry", held in 1994 at the National Academy of Sciences in Washington, published by the Board of Mathematical Sciences, National Research Council, 1997.) However, in the case of control theory for ODEs, the role played by differential geometry is quite different from the one that occurs in PDEs.