Abstract
An approach to analysis the structural identifiability (SI) of nonlinear dynamical systems under uncertainty was proposed. S-synchronizability condition of an input is the basis for the structural identifiability estimation of the nonlinear system. A method for obtaining a set containing information about the nonlinear part of the system wasproposed. The decision on SI of the system was based on the analysis of geometric frameworks reflected the state of the system nonlinear part. Geometric frameworks were defined on the specified set. Conditions for structural indistinguishability of geometric frameworks and local identifiability of the nonlinear part were obtained. It shown that a non-S-synchronizing input gives an insignificant geometric framework. This input is a sign of structural non-identifiability of the nonlinear system. The method for estimating the structural identifiability of the nonlinear system was proposed. We show that the structural identifiability is the basis for structural identification of the system. The structural identifiability degree was introduced, and the method of its estimation was proposed.
Highlights
Analysis of recent publications shows that the system identifiability is performed in a parametric space
Many authors study the parametric identifiability of nonlinear systems
In [2], an approach based on the sensitivity analysis of system output was applied to study identifiability and the analysis of experimental data was used for obtaining parametric identifiability conditions
Summary
Analysis of recent publications shows that the system identifiability is performed in a parametric space. The identifiability of a nonlinear system reduces to the parametric identifiability problem and is based on the application of various linearization methods This extensive field of research does not cover the structural identifiability problem of nonlinear dynamical systems in regarding to deciding on the structure (form, dependence) of the nonlinear system under uncertainty. The question not considered which an input having the excitement constancy property guarantees the structural identifiability of the system. This problem proposed in [6] first. An important question: “Which input having the excitement constancy property can provide guarantees the structural identifiability of the system” was not considered [6]. The main results obtained in this study can be considered as a generalization of those obtained in [6, 7]
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