带终点约束的线性随机控制系统的部分可控性及其在带跳跃的博弈控制系统中的应用

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2023-12-07 DOI:10.1137/22m1537114

Yuanzhuo Song

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引用次数: 0

摘要

SIAM 控制与优化期刊》，第 61 卷第 6 期，第 3635-3663 页，2023 年 12 月。摘要本文考虑了带终端约束的线性随机控制系统的部分可控性。借助后向随机微分方程 (BSDE)，我们得到了这种可控性的一些必要条件和充分条件。我们建立了基于博弈的控制系统（GBCS）的可控性、前向后向随机微分方程（FBSDE）的可控性和带终端约束的相关随机微分方程（SDE）的部分可控性之间的等价性。通过应用我们的结果，我们得到了带跳跃的 GBCS 可控性的一些必要条件和充分条件。然后，我们将仅由布朗运动驱动的 GBCS 和确定性 GBCS 嵌入到我们的带跳跃框架中。此外，我们还对张和郭之前的结果进行了覆盖和扩展。

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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The Partial Controllability of Linear Stochastic Control Systems with Terminal Constraints and Its Applications to Game-Based Control Systems with Jumps

SIAM Journal on Control and Optimization, Volume 61, Issue 6, Page 3635-3663, December 2023.
Abstract. In this paper, we consider the partial controllability of linear stochastic control systems with terminal constraints. Some necessary and sufficient conditions for this controllability are obtained with the help of backward stochastic differential equations (BSDEs). We establish the equivalence between the controllability of a game-based control system (GBCS), the controllability of a forward backward stochastic differential equation (FBSDE), and the partial controllability of a related stochastic differential equation (SDE) with terminal constraints. By applying our results, we obtain some necessary and sufficient conditions for the controllability of GBCSs with jumps. Then we embed the GBCSs driven only by Brownian motion and deterministic GBCSs into our framework with jumps. Previous results of Zhang and Guo are covered and extended.

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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.