基于观测器的分数阶热方程的指数稳定性

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Applied Mathematics and Optimization Pub Date : 2025-05-10 DOI:10.1007/s00245-025-10266-2

Hugo Parada

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引用次数: 0

摘要

本文研究了非局部分数阶热方程的指数稳定性。分数阶拉普拉斯式由奇异积分定义。利用分数阶拉普拉斯算子的谱特性和状态分解，考虑前N个模态和由有界算子定义的观测器，构造了反馈控制。研究了不同的配置，包括带内部观察的内部控制器和带外部观察的内部控制器。使用最近关于特征值的简单性的结果（Fall等人在Calc Var偏微分方程62(8):233,2023中），我们的一些稳定结果对\(s\in (0,1)\)有效，特别是对于\(s\in (0,1/2)\)，在这种情况下，分数热方程不是零可控的。

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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Observer-Based Exponential Stability of the Fractional Heat Equation

In this work, the exponential stability of the nonlocal fractional heat equation is studied. The fractional Laplacian is defined via a singular integral. Using the spectral properties of the fractional Laplacian and a state decomposition, a feedback control is constructed by considering the first N modes and an observer defined via a bounded operator. Different configurations are examined, including interior controller with interior observation, and interior controller with exterior observation. Using the recent result about the simplicity of the eigenvalues (Fall et al. in Calc Var Partial Differ Equ 62(8):233, 2023), some of our stabilization results are valid for \(s\in (0,1)\), in particular for \(s\in (0,1/2)\) in which case the fractional heat equation is not null controllable.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.