Identifiability and global estimability tools for dynamical systems

The identifiability and estimability properties of dynamical systems have been extensively studied in the literature. However, such approaches often focus on the sensitivity of system trajectories to perturbations in parameter values about some nominal parameter value. Relying on parameter sensitivity to assess parameter estimability can be misleading because the neighbourhood over which the sensitivity equations provide a good approximation of parameter influence can be very small. In this work, a complimentary notion of asymptotic sensitivity is defined. The asymptotic sensitivity is a measure of how much parameter values can be perturbed from their nominal value without affecting the number or type of steady state points available to the system. Such a notion is especially useful for systems that allow multiple steady states with different qualitative behaviour or where the asymptotic behaviour of the system is much better characterized than state trajectories. An efficient computational scheme for computing asymptotic sensitivity is presented. The proposed computational scheme is applied to a simple bioreactor system.