Determining the statistical properties of a robust control object identification algorithm using mixed correntropy

Identification process in stationary and non-stationary control objects has been investigated in this study. The task addressed is to construct mathematical models, to devise methods and procedures, and to develop programs focused on solving object identification problems. This paper tackles the issue of robust identification of control objects under the action of additive random noise of various statistical nature, in particular Gaussian and non-Gaussian noise. An approach to building identification algorithms based on the mixed correntropy criterion has been proposed, which combines the advantages of classical mean-square methods and information-theoretic optimality criteria. The use of Price's theorem made it possible to define convergence conditions for the robust identification algorithm in both stationary and non-stationary cases in the presence of Gaussian and non-Gaussian noise. The influence of algorithm parameters and noise characteristics on its dynamic properties has been established. Expressions for determining the optimal values of the algorithm's convergence parameter, which ensure the maximum convergence rate, have been derived. To confirm theoretical findings, simulation modeling was carried out, the results of which confirm the effectiveness of the proposed approach and its advantages compared to conventional identification methods, especially under conditions of non-Gaussian noise and nonstationarity, which indicates the feasibility of its use in adaptive and robust control systems. However, the resulting estimates are rather general and depend both on the degree of nonstationarity of the object and on the statistical characteristics of usable signals and disturbances, which are often unknown. Therefore, the results could be applied in practice if such information is available or when estimates of these characteristics are used