Qualitative validation and generalization in non-linear system identification

Abstract

Cell to cell mapping for the global analysis of non-linear systems is adopted to enable the qualitative validation of identified non-linear systems. The method provides a framework for the global analysis of a diverse range of non-linear systems, including continuous and discrete time systems, and non-linear identified models, and can be used to benchtest the effectiveness of various identification procedures. In the present study, the method is used to reveal the dynamic properties of a non-linear system, including the fixed points, periodic or aperiodic solutions and the corresponding stability properties. The orthogonal least squares algorithm (OLS) is then used to identify a parametric NARMAX model of the system. The resulting model is analysed using the same framework and the dynamic properties of the model are qualitatively compared with those of the original system. Based on the results of the validation, a modified selection criterion for the OLS algorithm is proposed, which incorporates the non-linear degree of the terms in the model complexity. The effectiveness of the new algorithm is demonstrated using examples.