  A mean field type control system is a dynamical system in the Wasserstein
space describing an evolution of a large population of agents with mean-field
interaction under a control of a unique decision maker. We develop the
viability theorem for the mean field type control system. To this end we
introduce a set of tangent elements to the given set of probabilities. Each
tangent element is a distribution on the tangent bundle of the phase space. The
viability theorem for mean field type control systems is formulated in the
classical way: the given set of probabilities on phase space is viable if and
only if the set of tangent distributions intersects with the set of
distributions feasible by virtue of dynamics.

Optimization and Control;Classical Analysis and ODEs;Probability