Structural Identifiability of Feedback Systems with Nonlinear Adulterating

We consider the structural identifiability estimation problem of Nonlinear Feedback Systems (NFS) with nonlinear adulterating. The problem of NFS Structural Identifiability (NFSI) has not been studied. Studying the NFSI problem guarantees the possibility of nonlinearity identification under uncertainty. Two cases of the adulterate influence are analyzed: (i) additive effect of feedback nonlinearity on the nonlinearity in the straight chain (ii) nonlinearity argument nonlinear adulterating in straight chain of the system. The basis for the identifiability estimation is: (a) the Geometric Frameworks (GF) analysis method reflecting properties of the nonlinear system; (b) structural frequency diagrams, and (c) the hierarchical immersion method. We obtain conditions of identifiability, unidentifiability and local identifiability for NFS. The influence of the nonlinear argument is analyzed on the system identifiability. We propose conditions for system unidentifiability verifying with a nonlinear argument of the function. The influence of the nonlinear argument is analyzed for estimating the system identifiability. Results are applicable in the synthesis of nonlinear control systems.