title: Quadratic and cubic Volterra polynomials: identification and application
metadata.name: dc.contributor.author
metadata.value: Solodusha, Svetlana V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-07-18T11:59:54Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-07-18T11:59:54Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Solodusha S. V. Quadratic and cubic Volterra polynomials: identification and application. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2018, vol. 14, iss. 2, pp. 131–144.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11702/spbu10.2018.205
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/10443
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Volterra kernels identification is the main problem in constructing an input-output type
  mathematical model of nonlinear dynamical system by a Volterra polynomial of Nth
  order. Currently, various algorithms for solving this problem are proposed. Usually, it is
  assumed that the decomposition of the dynamical system response y(t) into components
  is preliminarily performed. Each of components is due to the influence of the concrete
  integral term. In general, the separation problem is invariant with respect to a particular
  family of test actions, and the choice of amplitudes of the test signals used to identify the
  Volterra kernels is related to the necessary conditions for the solvability of the corresponding
  multidimensional integral equations in special classes of functions. In the present paper,
  existence theorems for solutions of two-dimensional and three-dimensional Volterra integral
  equations of the first kind are given. This result is obtained in terms of the amplitudes of
  the test signals. This will allow us to remove the arbitrariness in the choice of amplitudes
  in construction of the quadratic and cubic Volterra polynomials in the case when external
  action x(t) = (x1(t), x2(t))T is a vector function of time. Illustrative calculations are given
  through the dynamic reference systems.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при частичной финансовой поддержке Российского фонда фундаментальных исследований (грант №15-01-01425а) и Программы фундаментальных исследований Сибирского
  отделения РАН (проект № АААА-А17-117030310446-6).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Applied Mathematics. Computer Science. Control Processes;Volume 14; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: identification
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Volterra kernels
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: integral equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: mathematical modeling
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Quadratic and cubic Volterra polynomials: identification and application
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 05-Solodusha.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/10443/1/05-Solodusha.pdf
resources.format: Adobe PDF
resources.size: 339,92 kB