分数阶噪声驱动的离散时间控制系统的极大值原理及相关的倒向随机差分方程

IF 2.1 3区计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS

Systems & Control Letters Pub Date : 2025-07-21 DOI:10.1016/j.sysconle.2025.106202

Yuecai Han , Yuhang Li

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引用次数: 0

摘要

本文以分数阶布朗运动驱动系统的随机控制为激励，研究了分数阶噪声驱动的离散系统的随机最优控制问题，并将其应用于实际中带有“有色噪声”的控制问题。通过引入包含分数噪声和“底层”白噪声的倒向随机差分方程，得到了随机极大值原理。研究了后向随机差分方程的解。作为应用，考虑了线性二次情形，并求解了一个最优投资问题来说明主要结果。

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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Maximum principle for discrete-time control systems driven by fractional noises and related backward stochastic difference equations

In this paper, motivated by stochastic control for systems driven by fractional Brownian motion and the applications for control problem with “colored noises” in real-world, the stochastic optimal control for discrete-time systems driven by fractional noises is studied. A stochastic maximum principle is obtained by introducing a backward stochastic difference equation contains both fractional noises and the “underlying” white noises. The solution of the backward stochastic difference equations is also investigated. As an application, the linear quadratic case is considered and an optimal investment problem is solved to illustrate the main results.

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来源期刊

Systems & Control Letters 工程技术-运筹学与管理科学

CiteScore

4.60

自引率

3.80%

发文量

144

审稿时长

6 months

期刊介绍： Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.