Structural identifiability

In the area of system identification, a dynamical system is structurally identifiable if it is possible to infer its unknown parameters by measuring its output over time. This problem arises in many branch of applied mathematics, since dynamical systems (such as the ones described by ordinary differential equations) are commonly utilized to model physical processes and these models contain unknown parameters that are typically estimated using experimental data.

However, in certain cases, the model structure may not permit a unique solution for this estimation problem, even when the data is continuous and free from noise. To avoid potential issues, it is recommended to verify the uniqueness of the solution in advance, prior to conducting any actual experiments. The lack of structural identifiability implies that there are multiple solutions for the problem of system identification, and the impossibility of distinguishing between these solutions suggests that the system has poor forecasting power as a model. On the other hand, control systems have been proposed with the goal of rendering the closed-loop system unidentifiable, decreasing its susceptibility to covert attacks targeting cyber-physical systems.