Analysis of RHC for Stabilization of Nonautonomous Parabolic Equations Under Uncertainty

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-01-19 DOI:10.1137/23m1550876

Behzad Azmi, Lukas Herrmann, Karl Kunisch

引用次数: 0

Abstract

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 220-242, February 2024.
Abstract. Stabilization of a class of time-varying parabolic equations with uncertain input data using receding horizon control (RHC) is investigated. The diffusion coefficient and the initial function are prescribed as random fields. We consider both cases: uniform and log-normal distributions of the diffusion coefficient. The controls are chosen to be finite-dimensional and enter into the system as a linear combination of finitely many indicator functions (actuators) supported in open subsets of the spatial domain. Under suitable regularity assumptions, we study the expected (averaged) stabilizability of the RHC-controlled system with respect to the number of actuators. An upper bound is also obtained for the failure probability of RHC in relation to the choice of the number of actuators and parameters in the equation.

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不确定条件下稳定非自主抛物方程的 RHC 分析

SIAM 控制与优化期刊》第 62 卷第 1 期第 220-242 页，2024 年 2 月。摘要。利用后退地平线控制（RHC）研究了一类具有不确定输入数据的时变抛物线方程的稳定问题。扩散系数和初始函数被规定为随机场。我们考虑了两种情况：扩散系数的均匀分布和对数正态分布。控制被选择为有限维的，并作为有限多个支持空间域开放子集的指示函数（执行器）的线性组合进入系统。在适当的规则性假设下，我们研究了 RHC 控制系统的预期（平均）稳定性与执行器数量的关系。此外，我们还得出了 RHC 失效概率的上限，它与执行器数量和方程参数的选择有关。

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.