Identifiability of hybrid system models

Parameter estimation is an important tool in system modelling. However parameter estimation is difficult in many real-world application where continuous nonlinear dynamics interact with discrete-event dynamics. Nonlinear least-squares algorithms have been successfully applied. The paper establishes a connection between parameter identifiability and ill-conditioning of the least-squares algorithms. It is shown that a set of parameters is only identifiable if the trajectory sensitivities corresponding to those parameters are linearly independent. The importance of an appropriate choice of measurements is established.