Nonsmooth mean field games with state constraints

A level-set approach to the control of state-constrained McKean-Vlasov equations: application to renewable energy storage and portfolio selection

“…For example, the paper [18] solves mean-field control with delay and smooth expectation terminal constraint (and without dependence with respect to the law of the control). In the case of mean field games, state constraints are considered by [12,13,26,30,3]. In these cited works the state belongs to a compact set, which corresponds to a particular case of our constraints in distribution.…”

Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces

“…Motivated by this blooming interest for variational problems in measure spaces, several research groups have been investigating relevant generalisations of the core concepts of set-valued analysis to the setting of mean-field control [12,21,22,27,23,42,43,66], a lively trend that reached more recently other closely related topics such as mean-field games [6,31] and the study of sufficient conditions for the well-posedness of measure dynamics [44,67]. It is de facto widely accepted that the language of correspondences, differential inclusions and generalised gradients provides in many cases a synthetic and powerful framework in which most problems stemming from the calculus of variations, games and control theory can be encompassed, as supported e.g.…”