全耦合平均场控制系统的全局最优性原理

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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