杰弗里斯型过阻尼二阶线性系统的可接受性和可观测性

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-02-02 DOI:10.1137/22m1511680

Jian-Hua Chen, Xian-Feng Zhao, Hua-Cheng Zhou

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 1 期第 466-486 页，2024 年 2 月。摘要。我们研究了在希尔伯特空间环境下具有观测输出的 Jeffreys 型过阻尼二阶线性系统。状态方程来自一个过阻尼二阶线性偏微分方程，该方程类似于波，但被提出来描述热传导。它是采用热通量构成关系的杰弗里定律而非通常的傅里叶定律的结果。我们得到了系统观测算子的无限时可接受性和系统可观测性的充分条件。在一般情况下，我们从一阶 Cauchy 系统的无穷时可接受性出发，通过哈代空间方法获得无穷时可接受性。在状态方程中的算子为负定值的特殊情况下，我们采用半群方法推导出了无限时可容纳性和系统可观测性。文中给出了一些示例。

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Admissibility and Observability of Jeffreys Type of Overdamped Second Order Linear Systems

SIAM Journal on Control and Optimization, Volume 62, Issue 1, Page 466-486, February 2024.
Abstract. We study Jeffreys-type overdamped second order linear systems with observed outputs in the setting of Hilbert spaces. The state equation comes from an overdamped second order linear partial differential equation which is wave-like but was proposed to describe heat conduction. It results from adopting the Jeffreys law of constitutive relation for heat flux, rather than the usual Fourier law. Sufficient conditions for infinite-time admissibility of the system observation operator and system observability are obtained. In the general case, we obtain the infinite-time admissibility from that of the first order Cauchy system, which is done by employing the Hardy space approach. In the special case when the operator in the state equation is negative definite, we derive the infinite-time admissibility and system observability using a semigroup approach. Illustrative examples are given.

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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.