Abstract
Consideration was given to the method of statistical linearization of nonlinear stochastic plants on the basis of the dispersion identification theory for the Hammerstein class of models. The problem is notable for taking into account the dynamic nonlinearities of the plant. Models of statistical linearization were constructed with regard for the plant output noise of the kind of white noise and martingale sequence. Solution was obtained in the class of gradient recurrent identification algorithms. The necessary and sufficient conditions for strong consistency of the parameter estimates provided by these algorithms were presented. The results obtained were used for adaptive following of the plant output. Fitness of this method was substantiated by the example of a particular plant.
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REFERENCES
Prangishvili, I.V., Pashchenko, F.F., and Busygin, B.P., Sistemnye zakony i zakonomernosti v elektrodinamike, prirode i obshchestve (System Laws and Regularities in Electrodynamics, Nature, and Society), Moscow: Nauka, 2001.
Pashchenko, A.F. and Pashchenko, F.F., Statistical Linearization and Identification of Basically Nonlinear Systems, in Tr. Inst. Problem Upravlen., 1997, no. 5, pp. 103–121.
Kazakov, I.E. and Dostupov, B.G., Statisticheskaya dinamika nelineinykh avtomaticheskikh sistem (Statistical Dynamics of Nonlinear Automatic Control Systems), Moscow: Fizmatgiz, 1962.
Booton, R.C., Nonlinear Control Systems with Random Inputs, Trans. IRE Profess. Group Circuit Theory, 1954, vol. CT-1, no. 1, pp. 9–18.
Durgaryan, I.S. and Pashchenko, F.F., Dispersion Criterion for Statistical Optimization of Systems, Avtom. Telemekh., 1974, no. 12, pp. 46–52.
Pashchenko, F.F. and Bolkvadze, G.R., Statistical Linearization and Recurrent Dispersion Identification, Soobsh. AN Gruz. SSR, 1986, vol. 122, no. 3, pp. 509–512.
Dispersionnaya identifikatsiya (Dispersion Identiciation), Raibman, N.S., <nt>Ed.</nt>, Moscow: Nauka, 1981.
Medvedev, A.V., Neparametricheskie sistemy adaptatsii (Nonparametric Adaptation Systems), Novosibirsk: Nauka, 1983.
Juditsky, A., Hjalmarsson, H., Benveniste, A., et al., Nonlinear Black-Box Models in System Identifi-cation: Mathematical Foundations, Automatica, 1995, vol. 31, no. 12, pp. 1725–1750.
Bolkvadze, G.R., Identification of the Nonlinear Stochastic Hammerstein Plants, Avtom. Telemekh., 2002, no. 4, pp. 91–104.
Bolkvadze, G.R., Problem of Recurrent Dispersion Identification of Nonlinear Dynamic Plants, in Tr. Inst. Probl. Upravlen., 2001, vol. XIII, pp. 69–78.
Chen, H.F. and Gou, L., Necessary and Sufficient Conditions for Strong Consistency of Recursive Identification Algorithm, 7th IFAC/IFORS Symp. Identif. Syst. Parameter Estimation, York, 1985, pp. 1249–1253.
Guo, L., On Adaptive Stabilization of Time-varying Stochastic Systems, SIAM J. Contr. Optimiz., 1990, vol. 28, no. 6, pp. 1432–1451.
Stepanyants, S.L., Avtomatizatsiya tekhnologicheskikh protsessov ferrosplavnogo proizvodstva (Process Automation in Ferroalloy Production), Moscow: Metallurgiya, 1982.
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Bolkvadze, G.R. A Method of Dispersion Statistical Linearization of Nonlinear Stochastic Systems of the Hammerstein Class. Automation and Remote Control 65, 1046–1058 (2004). https://doi.org/10.1023/B:AURC.0000038712.73783.f7
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DOI: https://doi.org/10.1023/B:AURC.0000038712.73783.f7