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.
引用
收藏
页数：38
相关论文
共 54 条
  • [1] ON THE SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS ARISING IN MEAN FIELD TYPE CONTROL
    Achdou, Yves
    Lauriere, Mathieu
    [J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2015, 35 (09) : 3879 - 3900
  • [2] Ambrosio L, 2008, LECT MATH, P1
  • [3] Antonelli F., 1993, ANN APPL PROBAB, P777, DOI 10.1214/aoap/1177005363
  • [4] Axelrod R, 1984, EVOLUTION COOPERATIO
  • [5] On non-uniqueness and uniqueness of solutions in finite-horizon Mean Field Games
    Bardi, Martino
    Fischer, Markus
    [J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2019, 25
  • [6] Bellomo N., 2017, ACTIVE PARTICLES
  • [7] Linear-Quadratic Mean Field Games
    Bensoussan, A.
    Sung, K. C. J.
    Yam, S. C. P.
    Yung, S. P.
    [J]. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2016, 169 (02) : 496 - 529
  • [8] Bensoussan A, 2013, SPRINGERBRIEF MATH, P1, DOI 10.1007/978-1-4614-8508-7
  • [9] Vanishing viscosity solutions of nonlinear hyperbolic systems
    Bianchini, S
    Bressan, A
    [J]. ANNALS OF MATHEMATICS, 2005, 161 (01) : 223 - 342
  • [10] BOGACHEV V. I, 2007, MEASURE THEORY, VI, DOI 10.1007/978-3-540-34514-5
123456