Identifiability of differential algebraic equation systems

A mathematical model is identifiable if and only if there is a unique relationship between the value of each parameter and the input-output behaviour of the model. If a model is not identifiable then it is not possible to determine a unique set of parameter values that generates the observed model behaviour, regardless of the number and type of experiments performed. It is therefore important to check a model for identifiability a-priori. Otherwise, parameter estimates obtained through experiments may be inaccurate or non-informative. Inaccuracy in the parameter estimates can lead to poor design choices in scale-up of lab-scale systems, controller design and engineering practice.; Differential algebraic equation (DAE) systems are sets of equations that contain both ordinary differential equations and algebraic equations, and arise in chemical process models. Most of the tests for identifiability proposed in the literature have been proposed for ordinary differential equation (ODE) systems. Only the differential algebra method, although initially proposed for ODE systems, can accommodate the additional constraints found in DAE systems. However, this approach is restricted to certain classes of DAE system such as DAE system whose constituent mappings are all polynomial or meromorphic. Furthermore the use of the differential-algebra approach can be limited due to computational issues.; In this thesis several tests for the identifiability of DAE systems are proposed. The tests are based on the linearization of DAE systems about a rest point, and represent, in part, an extension of earlier results to the DAE case.; Two computationally efficient algorithms for testing the identifiability of linear time-invariant (LTI) DAE systems are presented. Also, a detailed framework for assessing the effect of initial conditions on the identifiability of LTI DAE systems is presented.; Finally, a differential algebra method proposed in this work is applied to a two-phase continuous reactor model. It is shown that even for this simple example, existing methods for assessing the identifiability of DAE models are not practical, while a linearization-based approach is. The reactor model is shown to be un-identifiable, and in addition, approaches for re-parameterization of the reactor model are discussed.