Structural Identifiability Evaluation of System with Nonsymmetric Nonlinearities

Abstract

The complexity of objects and control systems increases the requirements for mathematical models. The structural identifiability (SI) assessment of nonlinear systems is one of the identification problems. Until now, this problem solves by parametric methods using various approximation methods. This approach is not always effective under uncertainty. We apply an approach to SI estimation based on the analysis of virtual framework. There is an objects class whose properties describe by nonsymmetric nonlinearities. The paper generalizes and develops the virtual framework (VF) method for systems with asymmetric non-linearities. Requirements for the system input are formed based on the excitation constancy property and S-synchronizability. Considering S-synchronizability gives VF that most fully reflect nonlinear properties of the system. A method for designing virtual structures based on the measurement information analysis describes. Structural identifiability fundamentals described for systems with symmetric nonlinearities. Splitting of the initial nonlinear system obtains for the VF application. Two methods consider for evaluating SI systems with nonsymmetric nonlinearities (NN) and propose their development on systems with nonsymmetric nonlinearities. Virtual framework almost homotheticity conditions obtain for SI estimation. A NN class with parametric features considers and conditions for estimating their almost homotheticity obtain. Conditions of almost homothety and h-identifiability obtain for systems with NN. The detectability and recoverability proofed for virtual frameworks guaranteed the SI estimation under uncertainty. The conditions under which the nonsymmetric nonlinearity is hypothetical symmetric nonlinearity obtained. The described approach to the SI assessment is general. If the SI of specific nonlinear systems analyzes, then features these systems consider. These features require modification of proposed algorithms and procedures. SI evaluation examples of closed nonlinear systems given under uncertainty and of the excitation constancy fulfillment.