Abstract

The problem of parametric identification (determining the parameters of a system by observing solutions or functions of them) is one of the main problems in the applied theory of differential equations. When solving this problem, the property of local identifiability plays a crucial role. The presence of this property means that by observing solutions, it is possible to determine unambiguously the value of the system parameters in a neighborhood of the selected parameter. Previously, in the context of this problem, researchers mainly studied the case of a finite-dimensional parameter. The problem of local parametric identifiability in the case of an infinite-dimensional parameter has received much less attention. In this paper, we propose a new method for obtaining sufficient conditions for local parametric identifiability in the case of an infinite-dimensional parameter. When these conditions are met, an infinite-dimensional parameter belonging to certain classes is locally identified by observing the solution at a finite set of points. For systems with a linear dependence on the parameter, the genericity of the specified conditions is established.

中文翻译：

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具有无限维参数的微分方程组局部参数可辨识的条件

摘要

参数辨识问题（通过观察系统的解或函数来确定系统的参数）是微分方程应用理论中的主要问题之一。在解决这个问题时，局部可识别性起着至关重要的作用。该属性的存在意味着通过观察解，可以明确地确定所选参数邻域中的系统参数值。此前，针对该问题，研究人员主要研究了有限维参数的情况。无限维参数情况下的局部参数可辨识性问题受到的关注要少得多。在本文中，我们提出了一种新方法，用于在无限维参数的情况下获得局部参数可辨识性的充分条件。当满足这些条件时，通过观察有限点集的解来局部识别属于某些类的无限维参数。对于与参数具有线性相关性的系统，建立了指定条件的通用性。