Structural identifiability of non linear systems: an overview

Abstract

Structural identifiability is a fundamental prerequisite For parametric model identification. It concerns uniqueness of the parametric structure given a dynamical model and a set of inputloutput experimental dates. Proving structural identifiability propriety for non linear systems is considered until now a very difficult problem. Many approaches have been proposed in the litcrature but there isn't a generic method suitable for any non linear case. The main concern of this paper is to present an overview of different approaches used to test siruciural identifiability for non linear systems. Important aspects and difficulties of identifiability analysis will be reviewed and illustrated by an example of an actived sludge process characterized by rational polynomial non linearities and specified initial conditions.

A priori identifiability: An overview on definitions and approaches

“…The objective is to illustrate the differential algebra approach to test the algebraic identifiability of the parameter θ. From this perspective, it must be obtained an input/output relation in the general form (21). It turns out that the input/output relation reads:…”

“…The second objective of this paper is motivated by the matter on how identifiability can be tested. Several papers have investigated such an issue but they were restricted to special classes of systems (discrete ones in [20] or continuous ones in [21,10,11]). In the present paper, we give an overview for both deterministic continuous-time and discretetime systems and we point out the most relevant approaches according to the definitions.…”

The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

“…A brief overview on techniques for nonlinear identifiability is provided by Boubaker and Fourati [23], but see also the work by Godfrey and Fitch [24] for the use of a Taylor series expansion on examples in pharmacokinetics, publications by Ljung and Glad [25], and Saccomani et al [26] regarding computational approaches using differential algebra, and Evans et al [27] for a method based on the existence of a general nonlinear state transformation.…”

The use of a formal sensitivity analysis on epidemic models with immune protection from maternally acquired antibodies

“…Epidemic models of the type described by ( 1)-( 4) tend to be uncontrolled (free or autonomous) and nonlinear, requiring more complex methods of analysis over typical linear systems [22]. A brief overview on techniques for nonlinear identifiability is provided by Boubaker and Fourati [23], but see also the work by Godfrey and Fitch [24] for the use of a Taylor series expansion on examples in pharmacokinetics, publications by Ljung and Glad [25], and Saccomani et al [26] regarding computational approaches using differential algebra, and Evans et al [27] for a method based on the existence of a general nonlinear state transformation.…”