A systematic approach for doing an $\mathit{\text{a}}\mathit{\text{priori}}$ identifiability study of dynamical nonlinear models

This paper presents a method for investigating, through an automatic procedure, the (lack of) identifiability of parametrized dynamical models. This method takes into account constraints on parameters and returns parameters whose estimations make the model identifiable. It is based on i) an equivalence between an extension of the notion of identifiability and the existence of solutions of algebraic systems, ii) the use of symbolic computations for testing their existence. This method is described in details and is applied to two examples, of which the last one involves 12 parameters.