Asymptotic inversion of linear systems: A constructive causal state-space approach

IF 4.8 2区计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS

Automatica Pub Date : 2025-04-30 DOI:10.1016/j.automatica.2025.112354

Hamza Benadada, Michael Di Loreto, Damien Ébérard, Paolo Massioni

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引用次数: 0

Abstract

This article proposes a constructive design of an input observer for linear time invariant systems, grounded on asymptotical left inversion. Based on necessary and sufficient conditions for its existence, such a design leads to a causal and asymptotically convergent input estimation, for any initial condition and any input. Such design is iterative and decomposed as a forward–backward algorithm. Starting from a given initial system with an unknown input to be estimated, the forward algorithm leads, in a finite number of steps, to a system without any unknown input, called the target system. This forward algorithm requires iterative elementary algebraic operations for the system transformation. Subsequently, the backward algorithm includes a state estimation for the target system and computes an estimate of the unknown input, based on inverse algebraic operations used in the forward algorithm. As a final result, such input estimation is realized as a linear and causal dynamical system. An example illustrates the methodology.

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线性系统的渐近反演：一种建设性的因果状态空间方法

本文基于渐近左逆，提出了线性时不变系统输入观测器的构造性设计。根据其存在的充分必要条件，这种设计得到了对任意初始条件和任意输入的因果渐近收敛的输入估计。这种设计是迭代的，并分解为一种向前向后的算法。前向算法从一个给定的初始系统开始，有一个未知的输入待估计，在有限的步骤中，导致一个没有任何未知输入的系统，称为目标系统。该前向算法需要对系统变换进行迭代初等代数运算。然后，后向算法包括目标系统的状态估计，并基于前向算法中使用的逆代数运算计算未知输入的估计。最终，这种输入估计被实现为一个线性的、因果的动态系统。一个示例说明了该方法。

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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来源期刊

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.