隐马尔可夫跳变线性系统的h2静态输出反馈控制

Q4 Mathematics

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2020-01-01 DOI:10.56082/annalsarscimath.2020.1-2.405

A. M. de Oliveira, O. Costa

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引用次数: 1

摘要

在本章中，我们讨论了马尔可夫跳变线性系统在马尔可夫链和状态变量都部分观测的情况下的H2控制。控制器是静态的，依赖于一个观测变量，该变量在隐马尔可夫链的上下文中提供马尔可夫变量的唯一信息。我们提出了一种新的线性矩阵不等式设计条件，考虑了合适的系统矩阵的秩约束。接下来，我们研究了检测器提供马尔可夫链的完美估计并且所有状态对控制器可用的情况。最后，我们将这个结果与所谓的隐马尔可夫跳变线性系统的两步法进行比较，并给出了一个有故障的系统的学术实例。

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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ON THE H2 STATIC OUTPUT FEEDBACK CONTROL FOR HIDDEN MARKOV JUMP LINEAR SYSTEMS

In this chapter we discuss the H2 control for Markov jump linear systems in a context of partial observation of both the Markov chain and the state variable. The controller is static and depends on an observed variable that provides the only information of the Markov variable in a context of hidden Markov chains. We propose a new design condition in terms of linear matrix inequalities considering rank constraints in suitable system matrices that are easily fulfilled. Next we investigate the case in which the detector provides perfect estimations of the Markov chain and all the states are available to the controller. Finally we compare this result with the so-called two-step procedure for hidden Markov jump linear systems in an academic example of a system subject to faults.

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.