Vanishing viscosity in mean-field optimal control

被引：4
|
作者：
Ciampa, Gennaro [1 ]
Rossi, Francesco [2 ]
机构：
[1] Univ Milan, Dipartimento Matemat Federigo Enr, Via Cesare Saldini 50, I-20133 Milan, Italy
[2] Univ Padua, Dipartimento Matemat Tullio Levi Civita, Via Trieste 63, I-35131 Padua, Italy
来源：
ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2023年 / 29卷
基金：
欧洲研究理事会;
关键词：
Mean-field equations; optimal control of partial differential equations; vanishing viscosity; STOCHASTIC DIFFERENTIAL-EQUATIONS; CONTINUITY EQUATION; WASSERSTEIN SPACES; VELOCITY; LIMIT;
D O I：
10.1051/cocv/2023024
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
We show the existence of Lipschitz-in-space optimal controls for a class of mean-field control problems with dynamics given by a non-local continuity equation. The proof relies on a vanishing viscosity method: we prove the convergence of the same problem where a diffusion term is added, with a small viscosity parameter.By using stochastic optimal control, we first show the existence of a sequence of optimal controls for the problem with diffusion. We then build the optimizer of the original problem by letting the viscosity parameter go to zero.
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页数：38
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