Structural classification of non-linear systems by input and output measurements

It is desirable to know the internal structure of a non-linear system that is regarded as a 'black box'. The structural classification of the 'black box' is made from input and output relations. In this paper, the necessary conditions of structural classification are developed by the Volterra and Wiener theories and correlation analysis. A class of non-linear models in cascade is described by cross-correlation functions and Volterra and Wiener kernels. These conditions are first discussed in the frequency domain. Then the formulae of the conditions for structural identification in the time domain are obtained. Further, relations between structural information and the kernels are developed. Simulations are carried out that verify the authors' methods of structural testing. Next, some formulae for discriminating the feedback non-linear system's structure are newly developed. Furthermore, it is shown that the linear subsystem transfer functions and the non-linear subsystem parameters for these feedback non-linear systems can be estimated. Finally, the validity and sufficiency of the conditions for structural testing are discussed.