A Non-Linear MIMO System Identification Approach Based on the Multiple Maximal Correlation Technique

Abstract

Issues are considered that arise when solving problems of identification of stochastic systems and related to the application of nonlinear measures of dependence of random values. An approach to the identification of nonlinear multi-input / multi-output systems is proposed, based on the use of a measure of multiple dependence of the input and output processes of the system under study, the multiple maximal correlation. In the case of single-dimensional input/output systems, this measure of dependence corresponds to the maximum correlation. The approach proposed combines a non-parametric estimation of non-linear transformations of the system input and output vector-valued variables and parametric estimation of the linear system part. Meanwhile, the optimal non-linear transformations are just the ones that provide the maximum of the non-linear multiple correlation between the input and output vector-valued variables.