Set-Valued and Variational Analysis

, Volume 26, Issue 4, pp 993–1008

# Viability Theorem for Deterministic Mean Field Type Control Systems

• Yurii Averboukh
Article

## Abstract

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.

## Keywords

Viability theorem Mean field type control system Tangent distribution Nonsmooth analysis in the Wasserstein space

## Mathematics Subject Classification (2010)

49Q15 93C10 49J53 46G05 90C56

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