Nonlinear Observability and Identifiability: General Theory and a Case Study of a Kinetic Model for S. cerevisiae

Observability is a structural property of a control system defined as the possibility to deduce the state of the system from observing its input-output behaviour. The first part of this report presents a review of two different methods to test the observability of nonlinear control systems found in literature. The differential geometric and algebraic approaches have been applied to different classes of control systems. Both methods lead to the so-called rank test where the observability of a control system is determined by calculating the dimension of the space spanned by gradients of the Lie-derivatives of its output functions. It has been shown previously that for rational systems with n state-variables, only the first n − 1 Lie-derivatives have to be considered in the rank test. In this work, we show that this result applies for a broader class of analytic systems. The rank test can be used to determine parameter identifiability which is a special case of the observability problem. A case study is presented in which the parameter identifiability of a previously published kinetic model for the metabolism of S. cerevisiae (baker’s yeast) has been analysed. The results show that some of the model parameters cannot be identified from any set of experimental data. The general features of kinetic models of metabolism are examined and shown to allow a simplified identifiability analysis.