EXISTENCE OF OPTIMAL CONTROL FOR NONLINEAR FOKKER-PLANCK EQUATIONS IN L\bfone(RD).*

被引：2
作者：
Barbu, Viorel [1 ,2 ]
机构：
[1] Romanian Acad, Octav Mayer Inst Math, Iasi 700506, Romania
[2] AlI Cuza Univ, Iasi 700506, Romania
来源：
SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 2023年 / 61卷 / 03期
关键词：
Fokker-Planck equation; McKean-Vlasov equation; mild solution; mean field; STOCHASTIC DIFFERENTIAL-EQUATIONS;
D O I：
10.1137/22M1485243
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
This work is concerned with the existence of optimal controllers for the Bolza optimal control problem governed by the nonlinear Fokker-Planck equation in L1(Rd) with control input in the drift term. The solution to the control state system is a weak (mild) solution obtained from a vanishing viscosity approximation scheme. One obtains in particular the existence for the stochastic optimal control problem governed by McKean-Vlasov SDEs. For this problem, one proves the existence of a stochastic Markov optimal controller in feedback form.
引用
收藏
页码：1213 / 1230
页数：18
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