On a geometric approach to the structural identifiability problem and its application in a water quality case study

We present and apply an alternative method for the investigation of the well-known parameter identifiability question for non-linear system models. The method is based on a geometric analysis of the parametric output sensitivities and is, in fact, an application of the tools that are available in non-linear control theory to an augmented system, including the parametric output sensitivities. Accessibility Lie algebras are calculated that yield insight (through a simple rank test) in the controllability of this augmented system. The method is demonstrated in an example that is due to Dochain et al [4]. Results are confirmed by the method that has certain advantages in comparison to, for example, the Taylor series approach that seeks for identifiable combinations of parameters through inspection of the individual terms in a Taylor series expansion of the output signal, i.e. application of the well-known method of Pohjanpalo [15]. Parametric output sensitivities (as already noted by Dötsch and Van den Hof [5] and Peeters and Hanzon [13]) play a crucial role in identifiability analysis and we further elaborate on this insight in the current paper. Our goals are (i) to present an interesting method for addressing the (local) identifiability question for non-linear systems and (ii) to gain better understanding in the role of parametric state- and output sensitivities in the identifiability question that stems from an alternative perspective, and that has not been presented in the identification literature. Of course, we are aware of other algorithms and software that establishes an answer to the identifiability question, albeit from a different perspective, e.g. [19], but seek in the current paper mainly for another interpretation and computational framework to address the question of local identifiability, shedding some new light on the problem.