Integral Models in the Form of Volterra Polynomials and Continued Fractions in the Problem of Identifying Input Signals

Svetlana Solodusha (), Yuliya Kokonova and Oksana Dudareva
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Svetlana Solodusha: Melentiev Energy Systems Institute, Siberian Branch of the Russian Academy of Sciences, 664033 Irkutsk, Russia
Yuliya Kokonova: Matrosov Institute for System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, 664033 Irkutsk, Russia
Oksana Dudareva: Department of Applied Mathematics and Computer Science, Irkutsk National Research Technical University, 664074 Irkutsk, Russia

Mathematics, 2023, vol. 11, issue 23, 1-11

Abstract: The paper discusses the prospect of using a combined model based on finite segments (polynomials) of the Volterra integral power series. We consider a case when the problem of identifying the Volterra kernels is solved. The predictive properties of the classic Volterra polynomial are improved by adding a linear part in the form of an equivalent continued fraction. This technique allows us to distinguish an additional parameter—the connection coefficient α , which is effective in adapting the constructed integral model to changes in technical parameters at the input of a dynamic system. In addition, this technique allows us to take into account the case of perturbing the kernel of the linear term of the Volterra polynomial in the metric C [ 0 , T ] by a given value δ , implying the ideas of Volterra regularizing procedures. The problem of choosing the connection coefficient is solved using a special extremal problem. The developed algorithms are used to solve the problem of identifying input signals of test dynamic systems, among which, in addition to mathematical ones, thermal power engineering devices are used.

Keywords: polynomial Volterra integral equation; associated continued fraction; identification; nonlinear dynamical system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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