Feedback control for random, linear hyperbolic balance laws

IF 1.5 4区工程技术 Q2 ENGINEERING, MULTIDISCIPLINARY

International Journal for Uncertainty Quantification Pub Date : 2020-07-01 DOI:10.1615/int.j.uncertaintyquantification.2021037183

Stephan Gerster, M. Bambach, M. Herty, M. Imran

引用次数: 1

Abstract

We design the controls of physical systems that are faced by uncertainties. The system dynamics are described by random hyperbolic balance laws. The control aims to steer the system to a desired state under uncertainties. We propose a control based on Lyapunov stability analysis of a suitable series expansion of the random dynamics. The control damps the impact of uncertainties exponentially fast in time. The presented approach can be applied to a large class of physical systems and random perturbations, as~e.g.~Gaussian processes. We illustrate the control effect on a stochastic viscoplastic material model.

查看原文本刊更多论文

随机线性双曲平衡律的反馈控制

我们设计了面对不确定性的物理系统的控制。系统动力学由随机双曲平衡定律描述。该控制旨在引导系统在不确定的情况下达到所需的状态。我们提出了一种基于李雅普诺夫稳定性分析的控制方法，该方法适用于随机动力学的级数展开。该控制在时间上以指数级的速度衰减不确定性的影响。所提出的方法可以应用于一大类物理系统和随机扰动，例如高斯过程。我们说明了随机粘塑性材料模型的控制效果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

International Journal for Uncertainty Quantification ENGINEERING, MULTIDISCIPLINARY-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.60

自引率

5.90%

发文量

期刊介绍： The International Journal for Uncertainty Quantification disseminates information of permanent interest in the areas of analysis, modeling, design and control of complex systems in the presence of uncertainty. The journal seeks to emphasize methods that cross stochastic analysis, statistical modeling and scientific computing. Systems of interest are governed by differential equations possibly with multiscale features. Topics of particular interest include representation of uncertainty, propagation of uncertainty across scales, resolving the curse of dimensionality, long-time integration for stochastic PDEs, data-driven approaches for constructing stochastic models, validation, verification and uncertainty quantification for predictive computational science, and visualization of uncertainty in high-dimensional spaces. Bayesian computation and machine learning techniques are also of interest for example in the context of stochastic multiscale systems, for model selection/classification, and decision making. Reports addressing the dynamic coupling of modern experiments and modeling approaches towards predictive science are particularly encouraged. Applications of uncertainty quantification in all areas of physical and biological sciences are appropriate.