Statistical Linearization of MIMO Systems by Use of Quadratic Tsallis Mutual Information

Abstract

Problems of the stochastic system identification are analyzed, which are concerned with application of non-linear measures of dependence of random values and processes. Approaches are considered using a consistent in the A.N. Kolmogorov sense measure of dependence based on quadratic Tsallis mutual information. A constructive procedure of deriving a linear input/output model is proposed, which is a statistical equivalent of a non-linear multi-input/multi-output dynamic stochastic system driven by a Gaussian white-noise process. A keystone of such a procedure is the statistical linearization criterion that is the condition of the component-wise coincidence of quadratic Tsallis mutual information of the system input and output processes, from one hand side, and the input and output processes of the linearized model, from another hand side. This approach enables one to obtain explicit analytical expressions determining coefficients of the weight matrix of the linearized model. Meanwhile, the technique proposed is distribution free and does not require applying restricting assumptions on an explicit analytical form of the joint probability distribution of the system input and output processes, which may degenerate the substantial problem statement at all.