Viability Theorem for Deterministic Mean Field Type Control Systems

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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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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Krasovskii Institute of Mathematics and MechanicsYekaterinburgRussia
  2. 2.Ural Federal UniversityYekaterinburgRussia

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