Structural Identifiability of Systems with Multiple Nonlinearities
Keywords:structural identifiability, structure, geometric framework, nonlinearity, excitation constancy, importance graph, S-synchronizability, degree of non-identifiability
The structural identifiability (SI) problem considers for dynamical systems with multiple nonlinearities under uncertainty. It shows the widely used paradigm based on a priori parametric identifiability is not applicable in this case. The geometric framework (GF) is derivate from the system phase portrait and reflects the system nonlinear part properties under uncertainty. GF gives a conception of the system nonlinear part. The SI analysis problem interprets as a solution to the structural identification problem. The concept of S-synchronizability, which is the basis for estimation structural identifiability, introduce. Conditions of identifiability and structural identifiability are obtained. The constant excitation impact of input is studied on structural identifiability of the system. It shows that the input, which is constantly excited, can give the insignificant GF. Conditions are obtained for the existence of insignificant frameworks. Approaches are proposed to the estimation of structural identifiability systems with two nonlinearities and difficulties are noted. It is shown that a priori information is critical about the relation of variables. The approach is proposed to SI estimation based on the analysis of the influence graph.