Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls

Benoît Bonnet (1, 2) , Francesco Rossi (3)

1 PECASE - Pronostic-Diagnostic Et CommAnde : Santé et Energie
2 LIS - Laboratoire d'Informatique et des Systèmes (LIS) (Marseille, Toulon)
3 Dipartimento di Matematica "Tullio Levi-Civita"

In this paper, we provide a sufficient condition for the Lipschitz-in-space regularity for solutions of optimal control problems formulated on continuity equations. Our approach involves a novel combination of mean-field approximation results for infinite-dimensional multi-agent optimal control problems along with an existence result of locally optimal Lipschitz feedbacks. The latter is based in our context on a reformulation of a coercivity estimate in the language of the differential calculus of Wasserstein spaces.

Mots clés: Optimal control of continuity equations; regularity of minimizers; multi-agent systems; metric regularity; discretisation; differential calculus in Wasserstein spaces

Domaines: Automatique; Optimisation et contrôle [math.OC]

Benoît Bonnet, Francesco Rossi. Intrinsic Lipschitz Regularity of Mean-Field Optimal Controls. SIAM Journal on Control and Optimization, 2021, 59 (3), pp.2011-2046. ⟨hal-02271059v2⟩