Assessment of Computational Tools for Analysing the Observability and Accessibility of Nonlinear Models

Accessibility and observability are two properties of dynamic models that provide insights into the structural relationships between their input, output, and state variables. They are closely related to controllability and structural local identifiability, respectively. Observability and identifiability determine, respectively, the possibility of inferring the unmeasured state variables and parameters of a model from output measurements; accessibility and controllability describe the possibility of driving its state by changing its input. Analysing these structural properties in nonlinear models of ordinary differential equations can be challenging, particularly when dealing with large systems. Two main approaches are currently used for their study: one based on differential geometry, which uses symbolic computation, and another one based on sensitivity calculations that uses numerical integration. These approaches are implemented in two MATLAB (R2024b) software tools: the differential geometry approach in STRIKE-GOLDD, and the sensitivity-based method in StrucID. These toolboxes differ significantly in their features and capabilities. Until now, their performance had not been thoroughly compared. In this paper we present a comprehensive comparative study of them, elucidating their differences in applicability, computational efficiency, and robustness against computational issues. Our core finding is that StrucID has a substantially lower computational cost than STRIKE-GOLDD; however, it may occasionally yield inconsistent results due to numerical issues.