Abstract
New models of maps oriented to the solution of invariance problems in discrete dynamic systems that operate in conditions of deterministic chaos are proposed. The idea of K(E) transformation for quasi-stochastic sequences is developed based on these maps. The result is a method for the synthesis of discrete stabilization systems; this method, in combination with the principles of the classical theory of random processes, provides compensation for deterministic chaos and optimal filtering of stationary random noise.
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Nikolskii, V.A., Synthesis of Discrete Invariant Automatic Systems Using K(E) Transformation, Autom. Vych. Tekhn., 1969, no. 4, pp. 47–52.
Nikolskii, V.A. and Sevast’yanov, N.P., K(E) Transformation of Lattice Functions in Discrete System Study Problems, in Automatics and Electromechanics, Moscow: Nauka, 1973.
Nikolskii, V.A. and Sevast’yanov, N.P., Perturbation Filtering Method in Discrete Control Systems Based on K(E) Transformation, in Proceedings of 5th All-Union Meeting Invariance Theory and Its Application, Kiev: Naukova Dumka, 1979, pp. 337–346.
Nikolskii, V.A., Connection of Wiener Optimal Filtering Method for Invariance Principle Based on K(E) Transformation, VINITI Deposited Scientific Papers, no. 3, 1986.
Nikolskii, V.A., Application of Combined Control Principle in the Problem of On-Line Stocks Control, Ekonom. Matem. Met., 1980, vol. 16,issue 5, pp. 921–929.
Nikolskii, V.A., A Method of Step Control of Queue Length in Multiprocessor Numerical System with Variable Service Regime, Avtom. Vych. Tekhn., 1998, no. 6, pp. 61–70.
Malinetskii, G.G., Nonlinear Dynamics and Chaos, Moscow: KomKniga, 2006.
Neimark, Yu.I. and Landa, P.S., Stochastic and Chaotic Oscillations, Moscow: Nauka, 1997.
Kravtsov, V.A., Randomness as Predictability: the Concept of Partial Determinacy, Comm. Tech., 1990, vol. 35,issue 1.
Riznichenko, G.Yu. and Rubin, A.B., Mathematical Models of Biological Production Processes, Moscow: Izd. Mosk. Univ., 1993.
Nikolskii, V.A., Tsilker, B.Ya., and Pyatkov, V.P., Synthesis of Tracking Combined Control Systems Operating in Conditions of Regular Chaos, Avtom. Vych. Tekhn., 2009, no. 5, pp. 45–52.
Principe, J.C., Wang, L., Motter, M.A., Local Dynamic Modeling with Self-Organizing Maps and Applications to Nonlinear System Identification and Control, in Proceedings of IEEE, 1998, vol. 86, no. 11, pp. 2240–2258.
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Original Russian Text © V.A. Nikolskii, 2010, published in Avtomatika i Vychislitel’naya Tekhnika, 2010, No. 2, pp. 38–50.
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Nikolskii, V.A. Problem of invariance for discrete stabilization systems operating in conditions of regular chaos. Aut. Conrol Comp. Sci. 44, 85–95 (2010). https://doi.org/10.3103/S0146411610020045
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DOI: https://doi.org/10.3103/S0146411610020045