Abstract
We study the identification methods for the nonlinear dynamical systems described by Volterra series. One of the main problems in the dynamical system simulation is the problem of the choice of the parameters allowing the realization of a desired behavior of the system. If the structure of the model is identified in advance, then the solution to this problem closely resembles the identification problem of the system parameters. We also investigate the parameter identification of continuous and discrete nonlinear dynamical systems. The identification methods in the continuous case are based on application of the generalized Borel Theorem in combination with integral transformations. To investigate discrete systems, we use a discrete analog of the generalized Borel Theorem in conjunction with discrete transformations. Using model examples, we illustrate the application of the developed methods for simulation of systems with specified characteristics.
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References
V. Volterra, Theory of Functionals, Integral, and Integrodifferential Equations (Nauka, Moscow, 1982) [in Russian].
I. V. Boikov and N. P. Krivulin, Analytical and Numerical Methods for Identifying Dynamical Systems (Penzen. Gos. Univ., Penza, 2016) [in Russian].
Methods of Classical and Modern Theory of Autocontrol: School-Book, Vols. 1–5 (BaumannMoskov. Gos. Tekhn. Univ., Moscow, 2004) [in Russian].
I. V. Boikov, Analytical Methods for Identifying Dynamical Systems (Penzen. Politekh. Inst., 1992) [in Russian].
I. V. Boikov and N. P. Krivulin, “Determination of Time Characteristics of Linear Systems with Distributed Parameters,” Metrologiya No. 8, 3–14 (2012).
I. V. Boikov and N. P. Krivulin, “Parameter Recovery of Linear Systems Described by Differential Equations with Variable Coefficients,” Izmerit. Tekhnika No. 4, 6–11 (2013).
I.V. Boikov and N. P. Krivulin, “Identification of Discrete Dynamical Systems with Distributed Parameters,” Izv. Vyssh. Uchebn. Zaved. Povolzhsk. Region. Fiz.-Mat. Nauki 30 (2), 34–49 (2014).
I. V. Boikov and N. P. Krivulin, “Parametric Identification of Linear Dynamical Systems with Distributed Parameters,” Metrologiya No. 7, 13–24 (2014).
N. P. Krivulin, “Parameters Determination of Physical Processes Described by Partial Differential Equations with Variable Coefficients,” in Mathematical and Computer Modeling of Natural Scientific and Social Problems: Proceedings of 8th International Scientific-Technical Conference, Penza, May 26–30, 2014 (Izd. Penzen. Gos. Univ., Penza, 2014), pp. 172–178.
M. A. Shcherbakov, “Iterative Method of Optimal Nonlinear Filtration of Images,” Izv. Vyssh. Uchebn. Zaved. Povolzhsk. Region. Tekhn. Nauki 20 (4), 43–56 (2011).
K. A. Pupkov, V. I. Kapalin, and A. S. Yushchenko, Theoretical Foundations of Cybernetics (Function Series in Theory of Nonlinear Systems) (Nauka, Moscow, 1976) [in Russian].
A. M. Efros and A. M. Danilevskii, Operational Calculus and Contour Integrals (Gostekhizdat, Khar’kov, 1937) [in Russian].
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Original Russian Text © I.V. Boikov, N.P. Krivulin, 2018, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2018, Vol. XXI, No. 2, pp. 17–31.
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Boikov, I.V., Krivulin, N.P. Identification of Parameters of Nonlinear Dynamical Systems Simulated by Volterra Polynomials. J. Appl. Ind. Math. 12, 220–233 (2018). https://doi.org/10.1134/S1990478918020035
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DOI: https://doi.org/10.1134/S1990478918020035