title: Method for finding a solution to a linear nonstationary interval ОDЕ system
metadata.name: dc.contributor.author
metadata.value: Fominyh, Аlexander V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-07-14T13:22:09Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-07-14T13:22:09Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-06
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Fominyh А. V. Method for finding a solution to a linear nonstationary interval ОDЕ system. Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes, 2021, vol. 17, iss. 2, pp. 148-165.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https //doi.org/10.21638/11701/spbu10.2021.205
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/29867
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article analyses a linear nonstationary interval system of ordinary differential equations so that the elements of the matrix of the system are the intervals with the known lower and upper bounds. The system is defined on the known finite time interval. It is required to construct a trajectory, which brings this system from the given initial position to the given final state. The original problem is reduced to finding a solution of the differential inclusion of a special form with the fixed right endpoint. With the help of support functions, this problem is reduced to minimizing a functional in the space of piecewise continuous functions. Under a natural additional assumption, this functional is Gateaux differentiable. For the functional, Gateaux gradient is found, necessary and sufficient conditions for the minimum are obtained. Оn the basis of these conditions, the method of the steepest descent is applied to the original problem. Some examples illustrate the constructed algorithm realization.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: The main results of this paper (Sections 3 and 5) were obtained in IPME RAS and supported by Russian Science Foundation (project N 20-71-10032).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
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 17; Issue 2
metadata.lang: -
metadata.name: dc.subject
metadata.value: linear nonstationary interval system of ordinary differential equations
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: differential inclusion
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: support function
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: the steepest descent method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Method for finding a solution to a linear nonstationary interval ОDЕ system
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 148-165.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/29867/1/148-165.pdf
resources.format: Adobe PDF
resources.size: 464,66 kB