Strong left-invertibility and strong input-observability of nonlinear time-delay systems

In this paper, we study the problem of unknown inputs reconstruction for nonlinear time-delay systems. First we define two notions called strong left-invertibility and strong input-observability and the word "strong" is to address the causality properties of those two notions. Then necessa...

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Published inIEEE control systems letters Vol. 7; p. 1
Main Authors Chen, Yahao, Ghanes, Malek, Barbot, Jean-Pierre
Format Journal Article
LanguageEnglish
Published IEEE 01.01.2023
Subjects
Automatic
Control systems
Delays
Engineering Sciences
Heuristic algorithms
input-observability
left-invertibility
nonlinear systems
Observability
structure algorithm
Symbols
Terminology
time delays
Transfer functions
Online AccessGet full text
ISSN2475-1456
2475-1456
DOI10.1109/LCSYS.2022.3227130

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Abstract In this paper, we study the problem of unknown inputs reconstruction for nonlinear time-delay systems. First we define two notions called strong left-invertibility and strong input-observability and the word "strong" is to address the causality properties of those two notions. Then necessary and sufficient conditions for the strong left-invertibility and the strong input-observability are given under the algebraic framework proposed in 1. We find that a sequence of inputs submodules plays an important role for the strong left-invertibility of time-delay systems. A structure algorithm is provided to construct that sequence and to formulate an input reconstructor. At last, several examples are given to illustrate how to check the strong left-invertibility and the strong input-observability by applying the proposed structure algorithm, and to show how to recover the inputs via causal outputs and the initial value functions of states (strong left-invertibility) or only via causal outputs (strong input-observability).
AbstractList In this paper, we study the problem of unknown inputs reconstruction for nonlinear time-delay systems. First we define two notions called strong left-invertibility and strong input-observability and the word "strong" is to address the causality properties of those two notions. Then necessary and sufficient conditions for the strong left-invertibility and the strong input-observability are given under the algebraic framework proposed in 1. We find that a sequence of inputs submodules plays an important role for the strong left-invertibility of time-delay systems. A structure algorithm is provided to construct that sequence and to formulate an input reconstructor. At last, several examples are given to illustrate how to check the strong left-invertibility and the strong input-observability by applying the proposed structure algorithm, and to show how to recover the inputs via causal outputs and the initial value functions of states (strong left-invertibility) or only via causal outputs (strong input-observability).
Author Barbot, Jean-Pierre
Ghanes, Malek
Chen, Yahao
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SubjectTerms Automatic
Control systems
Delays
Engineering Sciences
Heuristic algorithms
input-observability
left-invertibility
nonlinear systems
Observability
structure algorithm
Symbols
Terminology
time delays
Transfer functions
Title Strong left-invertibility and strong input-observability of nonlinear time-delay systems
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https://hal.science/hal-03894297
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