Conditions of local parameter identifiability for systems of differential equations with an infinite-dimensional parameter

The problem of parameter identification (determining parameters of a system by observing solutions or functions of them) is one of the main problems of the applied theory of differential equations. The property of local identifiability plays the most important role in solving this problem. The presence of this property means that one can uniquely determine values of parameters of a system in a neighborhood of a particular parameter by observing solutions. Earlier the case of a finite-dimensional parameter was mostly studied in this issue. The problem of local parameter identifiability in the case of an infinite-dimensional parameter is less studied. In this paper we propose a new method for obtaining sufficient conditions for local parameter identifiability in the case of an infinite-dimensional parameter. Under these conditions an infinite-dimensional parameter belonging to certain classes is locally identifiable by observing a solution at a finite set of points. For system with linear dependence on a parameter we establish the genericity of the mentioned conditions.