Viscosity Solutions for McKean–Vlasov Control on a Torus

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-03-05 DOI:10.1137/22m1543732

H. Mete Soner, Qinxin Yan

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 2, Page 903-923, April 2024.
Abstract. An optimal control problem in the space of probability measures and the viscosity solutions of the corresponding dynamic programming equations defined using the intrinsic linear derivative are studied. The value function is shown to be Lipschitz continuous with respect to a smooth Fourier–Wasserstein metric. A comparison result between the Lipschitz viscosity sub- and supersolutions of the dynamic programming equation is proved using this metric, characterizing the value function as the unique Lipschitz viscosity solution.

查看原文本刊更多论文

环面上 McKean-Vlasov 控制的粘度解决方案

SIAM 控制与优化期刊》第 62 卷第 2 期第 903-923 页，2024 年 4 月。摘要研究了概率测度空间中的最优控制问题以及使用本征线性导数定义的相应动态程序方程的粘性解。研究表明，相对于光滑的傅里叶-瓦瑟斯坦度量，值函数是利普齐兹连续的。利用该度量证明了动态程序方程的 Lipschitz 粘度子解和超解之间的比较结果，将价值函数描述为唯一的 Lipschitz 粘度解。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.