有限样本保证线性动力系统的在线变化点检测

IF 4.8 2区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Lei Xin , George T.-C. Chiu , Shreyas Sundaram
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引用次数: 0

摘要

在线变化点检测的问题是检测时间序列属性的突然变化,最好是在这些变化发生后尽快检测。现有的在线变化点检测工作要么假定数据为 i.i.d.,要么侧重于渐近分析,要么没有提出检测精度和检测延迟之间权衡的理论保证,要么只适用于检测单个变化点。在这项工作中,我们研究了具有未知动态的线性动力系统的在线变化点检测问题,在这种情况下,数据具有时间相关性,系统可能有多个变化点。我们开发了一种与数据相关的阈值,可用于我们的检测,从而使误报概率达到预先设定的上限。我们进一步为检测到变化点的概率提供了一个基于有限样本的界限。我们的约束说明了我们算法中使用的参数如何影响检测概率和延迟,并为保证检测到变化所需的最小间隔时间提供了指导。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Online change points detection for linear dynamical systems with finite sample guarantees

The problem of online change point detection is to detect abrupt changes in properties of time series, ideally as soon as possible after those changes occur. Existing work on online change point detection either assumes i.i.d. data, focuses on asymptotic analysis, does not present theoretical guarantees on the trade-off between detection accuracy and detection delay, or is only suitable for detecting single change points. In this work, we study the online change point detection problem for linear dynamical systems with unknown dynamics, where the data exhibits temporal correlations and the system could have multiple change points. We develop a data-dependent threshold that can be used in our test that allows one to achieve a pre-specified upper bound on the probability of making a false alarm. We further provide a finite-sample-based bound for the probability of detecting a change point. Our bound demonstrates how parameters used in our algorithm affect the detection probability and delay, and provides guidance on the minimum required time between changes to guarantee detection.

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来源期刊
Automatica
Automatica 工程技术-工程:电子与电气
CiteScore
10.70
自引率
7.80%
发文量
617
审稿时长
5 months
期刊介绍: Automatica is a leading archival publication in the field of systems and control. The field encompasses today a broad set of areas and topics, and is thriving not only within itself but also in terms of its impact on other fields, such as communications, computers, biology, energy and economics. Since its inception in 1963, Automatica has kept abreast with the evolution of the field over the years, and has emerged as a leading publication driving the trends in the field. After being founded in 1963, Automatica became a journal of the International Federation of Automatic Control (IFAC) in 1969. It features a characteristic blend of theoretical and applied papers of archival, lasting value, reporting cutting edge research results by authors across the globe. It features articles in distinct categories, including regular, brief and survey papers, technical communiqués, correspondence items, as well as reviews on published books of interest to the readership. It occasionally publishes special issues on emerging new topics or established mature topics of interest to a broad audience. Automatica solicits original high-quality contributions in all the categories listed above, and in all areas of systems and control interpreted in a broad sense and evolving constantly. They may be submitted directly to a subject editor or to the Editor-in-Chief if not sure about the subject area. Editorial procedures in place assure careful, fair, and prompt handling of all submitted articles. Accepted papers appear in the journal in the shortest time feasible given production time constraints.
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