对于具有混合延迟的落后随机系统,一个足够的最大原则
Heping Ma1, Hui Jian2, Yu Shi3
1School of Science, Hubei University of Technology, Wuhan 430068, China.
Mathematical biosciences and engineering : MBE
|December 21, 2023
概括
这项研究开发了对具有多次时间延迟的倒置随机微分方程的最佳控制. 它建立了足够的最佳条件,并证明了它们对线性二次数系统的应用,解释了延迟效应.
科学领域:
- 随机分析 随机分析
- 最佳控制理论 最佳控制理论
- 数字模拟 数字模拟
背景情况:
- 逆向随机微分方程 (BSDE) 在金融和控制方面至关重要.
- 整合时间延迟 (离散,移动平均值,噪音记忆) 复杂化BSDE的分析和控制.
- 现有的方法经常在BSDE中与多种复杂的延迟类型作斗争.
研究的目的:
- 为具有三种延迟的随机系统建立足够的最佳条件.
- 引入和验证用于分析这些延迟的BSDE的新型时间高级附加方程.
- 将开发出来的理论应用于线性二次倒置随机系统,并分析延迟影响.
主要方法:
- 对于延迟的BSDE来说,足够的最佳条件的导出.
- 介绍两个相当的时间推进的随机微分方程 (附加方程).
- 马利亚文微积分用于处理附加方程中的导数.
- 模拟延迟随机微分方程的离散化技术.
主要成果:
- 为所研究的随机系统建立一个足够的最佳条件.
- 证明两种类型的时间推进的附加方程之间的等价性.
- 对于线性二次倒置随机系统来说,获得了明确的最佳控制.
- 数字模拟说明了时间延迟对控制结果的影响.
结论:
- 拟议的框架有效地解决了多次延迟的BSDE的最佳控制.
- 开发的相连方程为分析复杂的延迟随机系统提供了可行的工具.
- 时间延迟对这些系统的最佳控制策略和解决方案产生重大影响.
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