Identification of quadratic complex-valued dynamic neighborhood models on clustereddata and with outclustering

Neighborhood models and their modifications used to model various distributed systems and processes. The study considers a quadratic complex-valued dynamic neighborhood model in which the parameters, inputs and states are complex numbers, and its definition is given. The model functions in discrete time. An example of a complex-valued dynamic neighborhood model consisting of three nodes shown, for which the graph of the structure and the functions of the intersection of states given in general form. A special case of recalculation functions for a quadratic model is also considered. An algorithm for identifying a complex-valued dynamic neighborhood model whose parameters are determined by the least squares method given. A general view of the matrices of a system of linear equations for finding the parameters of a quadratic model shown. Matrices are given and identification performed for the considered example of a neighborhood model. The root-mean-square and average reduced identification errors are found. The paper also considers the identification of a complex-valued dynamic neighborhood model on clustered data. Clustering performed using complex data sets by the k-means method. The proposed identification algorithms implemented in the form of a program in the Mathcad package, with the help of which the results of identification of a quadratic complex-valued dynamic neighborhood model on clustered data and without clustering are compared.