Identifiability of a Family of Dynamical Systems Application to Crops Identification

Abstract

In this paper we consider the problem of identifying a system among a family of given systems. Thus, from measurements collected on an unidentified system but that is part of a family of known model systems, we seek to determine this unidentified system. This differs from identifying the parameters of a given system through experimental observations. The determination (identification) in a given family not always being possible, we refer to the identifiable family as any family for which this identification is possible. We thus introduce the concept of identifiability of a family of systems through a given measurement function. For localized linear systems we give algebraic characterizations that use the notion of system observability. We then propose algorithms which, in case of identifiability of the family and by a process of elimination, identify the system to which the collected measurements correspond. We have given some examples to illustrate these algorithms. We have also added an exemplified extension to discrete localized systems.