Systems of first-order partial differential inclusions -- solutions of which are feedbacks governing viable trajectories of control systems -- are derived. A variational principle and an existence theorem of a (single-valued contingent) solution to such partial differential inclusions are stated. To prove such theorems, tools of set-valued analysis and tricks taken from viability theory are surveyed.
This paper is the text of a plenary conference to the World Congress on Nonlinear Analysis held at Tampa, Florida, August 19-26, 1992
