Identification of Structural Models as a Problem of Group Representation Theory

It has been shown that symmetries of moment functions of stochastic processes play an important role in identification of systems. They provide the group-theoretic method of choice of the model structure and model parameters. In the first stage the group-theoretic analysis of some fundamental concepts of stochastic dynamics: stochastic processes and functional series of Volterra-Wiener type has been undertaken. The analysis of group representations of the moment functions of order m for stochastic processes is the basic, original concept of the work. The following groups: symmetric Sm, special affine SAff(m), general linear GL(n, R), GL(n,C) and their subgroups play the main role in the models. In the second stage the informational entropy has been introduced as a measure of the randomness in the identified models. The group-theoretic approach underlines the unity of the nonlinear system identification and leads to useful engineering results in the range of the second-order (stochastic) theory.