子扩散驱动的全耦合前后向随机微分方程的随机最大原则

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-09-03 DOI:10.1137/23m1620168

Shuaiqi Zhang, Zhen-Qing Chen

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引用次数: 0

摘要

SIAM 控制与优化期刊》，第 62 卷第 5 期，第 2433-2455 页，2024 年 10 月。摘要。我们研究了由反常子扩散驱动的全耦合前向后向随机微分方程的最优随机控制问题，该问题具有确定性控制和随机控制的非难混合特征。随机最大原则（SMP）和充分随机最大原则都是通过使用凸变方法得到的。论文最后将本文的主要结果应用于亚扩散环境中的线性二次问题，并对该问题进行了显式求解。

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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Stochastic Maximum Principle for Fully Coupled Forward-Backward Stochastic Differential Equations Driven by Subdiffusion

SIAM Journal on Control and Optimization, Volume 62, Issue 5, Page 2433-2455, October 2024.
Abstract. We study optimal stochastic control problems for fully coupled forward-backward stochastic differential equations driven by anomalous subdiffusion, which have nontrivial mixed features of deterministic and stochastic controls. Both the stochastic maximum principle (SMP) and sufficient SMP are obtained by using a convex variational method. The paper ends with an application of the main results of this paper to a linear quadratic problem in the subdiffusive setting, which is solved explicitly.

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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.