确定性系统子空间辨识的非渐近误差分析

IF 2.5 3区 计算机科学 Q3 AUTOMATION & CONTROL SYSTEMS
Shuai Sun
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引用次数: 0

摘要

子空间辨识方法(SIM)在离散多输入多输出(MIMO)线性时不变(LTI)系统辨识中得到了广泛的应用。本文重点分析了基于单一有限长度输入/输出样本轨迹,在两个统一的SIMs下,状态空间模型中系统矩阵和相应的系统极点的摄动误差。具体来说,我们推导了这些误差的非渐近上界,提供了跨各种SIM变体的统一视角。此外,我们证明了当状态与输出维数之比n/m很大时,无论系统参数如何,MIMO系统的SIMs都是病态的。最后,通过数值实验验证了模拟的非渐近性和病态性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Non-asymptotic error analysis of subspace identification for deterministic systems
The subspace identification method (SIM) has been extensively employed in the identification of discrete-time multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems. This paper focuses on the analysis of perturbation errors for the system matrices in state-space models and the corresponding system poles, under two unified SIMs, based on a single finite-length input/output sample trajectory. Specifically, we derive non-asymptotic upper bounds on these errors, providing a unified perspective across various SIM variants. Furthermore, we prove that SIMs become ill-conditioned for MIMO systems when the state-to-output dimensionality ratio n/m is large, regardless of system parameters. Finally, numerical experiments are conducted to validate the non-asymptotic results and the ill-conditionedness of SIMs.
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来源期刊
Systems & Control Letters
Systems & Control Letters 工程技术-运筹学与管理科学
CiteScore
4.60
自引率
3.80%
发文量
144
审稿时长
6 months
期刊介绍: Founded in 1981 by two of the pre-eminent control theorists, Roger Brockett and Jan Willems, Systems & Control Letters is one of the leading journals in the field of control theory. The aim of the journal is to allow dissemination of relatively concise but highly original contributions whose high initial quality enables a relatively rapid review process. All aspects of the fields of systems and control are covered, especially mathematically-oriented and theoretical papers that have a clear relevance to engineering, physical and biological sciences, and even economics. Application-oriented papers with sophisticated and rigorous mathematical elements are also welcome.
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