Controllability and observability of control systems under uncertainty

This report surveys the results of nonlinear systems theory (controllability and observability) obtained at IIASA during the last three summers. Classical methods based on differential geometry require some regularity and fail as soon as state-dependent constraints are brought to bear on the controls, or uncertainty and disturbances are involved in the system. Since these important features appear in most realistic control problems, new methods had to be devised, whcih encompass the classical ones, and allow the presence of a priori feedback into the control systems. This is now possible thanks to new tools, in the development of which IIASA played an important role: differential inclusions and set-valued analysis.