Geodesic
The problem of identifying the input signal of dynamic systems modeled by Volterra polynomials
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 83-90

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In this paper, we consider one class of Volterra equations of the first kind that appear in the problem of identifying the input signal of a dynamic system. We discuss an approach to the approximate solution of Volterra polynomial equations that model nonlinear dynamics by integro-power Volterra series. A method for constructing a numerical solution using the Newton–Kantorovich iterative process is proposed. Based on standard quadrature methods and the product integration method, we obtain calculation formulas.
Mots-clés : identification
Keywords: nonstationary dynamical system, polynomial Volterra equation of the first kind, Newton–Kantorovich method 
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     author = {S. V. Solodusha and Yu. I. Kokonova},
     title = {The problem of identifying the input signal of dynamic systems modeled by {Volterra} polynomials},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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     publisher = {mathdoc},
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S. V. Solodusha; Yu. I. Kokonova. The problem of identifying the input signal of dynamic systems modeled by Volterra polynomials. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the 5th International Conference "Dynamical Systems and Computer Science: Theory and Applications" (DYSC 2023). Irkutsk, September 18-23, 2023, Tome 234 (2024), pp. 83-90. http://geodesic.mathdoc.fr/item/INTO_2024_234_a10/