全耦合平均场控制系统的全局最优性原理

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Acta Mathematicae Applicatae Sinica, English Series Pub Date : 2024-03-27 DOI:10.1007/s10255-024-1112-9

Tao Hao

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引用次数: 0

摘要

本文涉及全耦合均场控制系统的全局最优性原理。一阶和二阶变分方程都是全耦合均值场线性 FBSDE。通过引入一种新的线性关系，我们成功地解耦了全耦合一阶变分方程。我们给出了 Yε 的新二阶展开式，它可以在均值场框架中很好地工作。基于这一结果，我们证明了随机最大原则。提供了与受控均场随机微分方程随机最大原理的比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Global Optimality Principle for Fully Coupled Mean-field Control Systems

This paper concerns a global optimality principle for fully coupled mean-field control systems. Both the first-order and the second-order variational equations are fully coupled mean-field linear FBSDEs. A new linear relation is introduced, with which we successfully decouple the fully coupled first-order variational equations. We give a new second-order expansion of Y^ε that can work well in mean-field framework. Based on this result, the stochastic maximum principle is proved. The comparison with the stochastic maximum principle for controlled mean-field stochastic differential equations is supplied.

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来源期刊

Acta Mathematicae Applicatae Sinica, English Series 数学-应用数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Acta Mathematicae Applicatae Sinica (English Series) is a quarterly journal established by the Chinese Mathematical Society. The journal publishes high quality research papers from all branches of applied mathematics, and particularly welcomes those from partial differential equations, computational mathematics, applied probability, mathematical finance, statistics, dynamical systems, optimization and management science.