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.
Citation:
I. V. Boikov, N. P. Krivulin, “Identification of parameters of nonlinear dynamical systems simulated by Volterra polynomials”, Sib. Zh. Ind. Mat., 21:2 (2018), 17–31; J. Appl. Industr. Math., 12:2 (2018), 220–233
\Bibitem{BoyKri18}
\by I.~V.~Boikov, N.~P.~Krivulin
\paper Identification of parameters of nonlinear dynamical systems simulated by Volterra polynomials
\jour Sib. Zh. Ind. Mat.
\yr 2018
\vol 21
\issue 2
\pages 17--31
\mathnet{http://mi.mathnet.ru/sjim996}
\crossref{https://doi.org/10.17377/sibjim.2018.21.201}
\elib{https://elibrary.ru/item.asp?id=35459097}
\transl
\jour J. Appl. Industr. Math.
\yr 2018
\vol 12
\issue 2
\pages 220--233
\crossref{https://doi.org/10.1134/S1990478918020035}
\elib{https://elibrary.ru/item.asp?id=35498165}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85047877887}
Linking options:
https://www.mathnet.ru/eng/sjim996
https://www.mathnet.ru/eng/sjim/v21/i2/p17
This publication is cited in the following 4 articles:
Tiancheng Zong, Junhong Li, Guoping Lu, “Parameter identification of dual-rate Hammerstein-Volterra nonlinear systems by the hybrid particle swarm-gradient algorithm based on the auxiliary model”, Engineering Applications of Artificial Intelligence, 117 (2023), 105526
I. V. Boikov, N. P. Krivulin, S. V. Abramov, V. P. Malanin, V. V. Kikot, “Recovery of the input signals of eddy-current displacement transducers under thermal-shock actions”, Meas. Tech., 61:11 (2019), 1118–1125
Ilia Boikov, Nikolay Krivulin, 2019 XXI International Conference Complex Systems: Control and Modeling Problems (CSCMP), 2019, 658