Exact Controllability for a Refined Stochastic Wave Equation

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS SIAM Journal on Control and Optimization Pub Date : 2024-02-07 DOI:10.1137/22m1537680

Zhonghua Liao, Qi Lü

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 563-580, February 2024.
Abstract. In this paper, we obtain the exact controllability for a refined stochastic wave equation with three controls by establishing a novel Carleman estimate for a backward hyperbolic-like operator. Compared with the known result [Q. Lü and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021], the novelty of this paper is twofold: (1) Our model contains the effects in the drift terms when we put controls directly in the diffusion terms, which is more sensible for practical applications; (2) We provide an explicit description of the waiting time which is sharp in the case of dimension one and is independent of the coefficents of lower terms.

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精炼随机波方程的精确可控性

SIAM 控制与优化期刊》第 62 卷第 1 期第 563-580 页，2024 年 2 月。摘要本文通过建立后向双曲样算子的新颖卡勒曼估计，得到了具有三个控制的精炼随机波方程的精确可控性。与已知结果 [Q.Lü and X Zhang, Mathematical Control Theory for Stochastic Partial Differential Equations, Springer, Cham, Switzerland, 2021]相比，本文的新颖之处有两点：(1) 当我们直接在扩散项中加入控制时，我们的模型包含了漂移项中的效应，这对实际应用更有意义；(2) 我们提供了等待时间的显式描述，该描述在维数为一的情况下是尖锐的，且与较低项的系数无关。

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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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.