Identifiability of Classes of Input-Output Systems

The identifiability of abstract classes of input-output systems from a finite set of input-output experiments is considered. Both exact and approximate identifiability are addressed. Here, "system" means a function from an input space to an output space. With only linear structure on the output space and on the class of unknown systems, it is shown that a finite-dimensional class of systems is always exactly identifiable, and the identified systems have the form of interpolations on the input-output data. With linear and topological structure on the input space, output space, and space of unknown systems we state conditions under which a class of unknown systems can be identified to within a specified tolerance by interpolative identification models.