Statistical Linearization of Multivariable Systems with a Criterion Based on the Rényi Entropy

The paper analyzes some problems appearing under identification of stochastic systems and concerned with applying measures of non-linear dependence of random processes (values). An approach utilizing such a measure based on the quadratic Rényi entropy is considered. A constructive procedure of deriving a linear input/output model that is a statistical equivalent of a multivariable stochastic system driven by a Gaussian white-noise process. A key issue of such a procedure is applying the condition of the component-wise coincidence of the mentioned measure based on the Rényi entropy of the order 2 of the input and output processes of the system and the input and output processes of the linearized model as the statistical linearization criterion. The approach enables one to obtain explicit analytical expressions determining elements of the weight matrices of the linearized model. The paper has been supported by a grant of the Russian Foundation for Basic Researches (RFBR): project 12-08-01205-a.