2016/12/31 by Yurii Averboukh, Averboukh, Yurii · 1 citation
Mathematics · #46G05 #49J53 #49Q15 #90C56 #93C10 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #math.CA #math.OC #math.PR #msc:46G05 #msc:49J53 #msc:49Q15 #msc:90C56 #msc:93C10
paper · pdf · doi:10.48550/arxiv.1701.00089
20 pages
arxiv created 2018/01/30 · arxiv updated 2018/02/01
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.