Finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation

IF 2.1 3区 计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS
Yu-Shuo Shang , Ze-Hao Wu , Hua-Cheng Zhou
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引用次数: 0

Abstract

In this article, we investigate the finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation with nonlinear multiplicative noise and non-local sensing measurement. We adopt the modal decomposition to divide the system into two subsystems: one unstable with finite positive eigenvalues and the other essentially stable. We design the controller for the unstable subsystem by dynamic extension and demonstrate that the proposed controller actually leads to the resulting closed-loop system to be well-posed and exponentially stable, both in the mean square and almost sure senses. Finally, some numerical simulations are performed to illustrate the effectiveness of the proposed method.
一维随机热方程的有限维观测器边界控制
本文研究了具有非线性乘性噪声和非局部感知测量的一维随机热方程的有限维观测器边界控制。我们采用模态分解将系统分为两个子系统:一个具有有限正特征值的不稳定子系统和另一个基本稳定子系统。我们通过动态扩展设计了不稳定子系统的控制器,并证明了所提出的控制器实际上导致闭环系统在均方和几乎确定意义上都是适定的和指数稳定的。最后,通过数值仿真验证了所提方法的有效性。
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
Systems & Control Letters
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.
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