A STOCHASTIC MAXIMUM PRINCIPLE FOR GENERAL MEAN-FIELD SYSTEM WITH CONSTRAINTS

被引：0

作者：

Meherrem, Shahlar ^{[1
,2
]}

Hafayed, Mokhtar ^{[3
]}

机构：

[1] Yasar Univ, Fac Sci & Letters, Dept Math, Izmir, Turkiye

[2] Azerbaijan Natl Acad Sci, Inst Control Syst, Baku, Azerbaijan

[3] Biskra Univ, Lab Math Anal Probabil & Optimizat, POB 145, Biskra 07000, Algeria

来源：

NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION | 2025年 / 15卷 / 03期

关键词：

Stochastic control; stochastic differential equations of mean-field type; variational principle; second-order derivative with respect to measures; maximum principle; OPTIMALITY CONDITIONS; EQUATIONS; DELAY;

D O I：

10.3934/naco.2024006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the optimal control of a general mean-field stochastic differential equation with constraints. We establish a set of necessary conditions for the optimal control, where the coefficients of the controlled system depend, nonlinearly, on both the state process as well as of its probability law. The control domain is not necessarily convex. The proof of our main result is based on the first-order and second-order derivatives with respect to measure in the Wasserstein space of probability measures, and the variational principle. We prove Peng's type necessary optimality conditions for a general mean-field system under state constraints. Our result generalizes the stochastic maximum principle of Buckdahn et al. [2] to the case with constraints.

引用

页码：565 / 578

页数：14

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