Conditions for Local Parameter Identifiability for Systems of Differential Equations with an Infinite-Dimensional Parameter

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.