Identifiabilities and nonlinearities

A parametric model structure is (globally) identifiable if the parameter vector associated with a given input-output behavior is unique. If this is not the case, careless estimation of this vector from experimental data may lead to completely erroneous results. (The situation is similar when unobserved state variables have to be estimated from the outputs.) The effect of two types of nonlinearity of the output (with respect to the parameters and to the inputs) on structural identifiability is described. Various methods to test state space models for identifiability are presented. They apply to models that are nonlinear with respect to the parameters and may be linear or not with respect to the inputs. Their use is illustrated on simple examples and an actual problem in chemical engineering. Advantages and limitations of the existing techniques are evidenced. Relationships between structural identifiability and practical identifiability, i.e. the ability to actually estimate the parameters of the model from experimental data, are considered, as well as techniques available to design an experiment so as to make the parameters of interest as identifiable as possible.

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