The numerical method of the solution of the tensor equations Kron for two-level
hierarchical system in the presence of relevant communications of mutual influence between
its components is considered. The idea of a method consists that the detailed account of
communications of interference, actually and causing difficulties of the decision of the given
equations, is substituted for typical algorithms of optimization of coordination type. The
choice of type of algorithm is anticipated a quantitative estimation of degree of a mismatch of
parameters of the components, the system theory of the conflict based on ideas. It is shown
that all variety of mismatches can be reduced to three typical variants: to an essential
mismatch, practical absence of local mismatches and an insignificant mismatch on minor
questions. In the first variant for normal functioning of system it is required, that in it system
interests dominated. In the second variant the decision of problems can be given on level of
components of system. In the third variant to eliminate mismatches it is possible on the basis
of parity of system and local interests. Algorithms of optimization corresponding to these
variants are described: at domination of system interests, at domination of local interests and
at parity of interests. The method is realized in the form of a program complex on the basis of
Visual Basic programming systems, S ++ and Delphi. Numerical experiment proves
convergence of algorithms of optimization. The method can find practical application as the
tool of support of decision-making at management difficult dynamic system of hierarchical
type
1. Kron G. Primenenie tenzornogo analiza v elektrotekhnike. – M.: Nauka,
1955. – 156 p.
2. Kron G. Tenzornyy analiz setey. – M.: Sov. radio, 1978. – 720 p.
3. Novosel'tsev V.I., Kochedykov S.S., Orlova D.E. Tenzornyy analiz Krona i
ego prilozheniya / Pod red. V.I. Novosel'tseva. – Voronezh: IPTs
«Nauchnaya kniga», 2017. – 220 p.
4. Mikheeva T.I., Mikheev S.V., Zolotovitskiy A.V. Avtomatizirovannaya
sistema kontrolya i upravleniya dorozhnym dvizheniem // Matematika.
Komp'yuter. Obrazovanie: sb. nauchn. tr. / Dubna: MGU, - 2008. pp. 207-
214.
5. Mesarovich M., Mako D., Takakhara I. Teoriya ierarkhicheskikh i
mnogourovnevykh sistem / Per. s angl. – M.: Mir, 1973. – 344 p
6. Aliev R.A., Liberzon M.I. Metody i algoritmy koordinatsii v
promyshlennykh sistemakh upravleniya. – M.: Ekonomika, 1987. -168.
7. Novosel'tsev V.I., Tarasov B.V. Sistemnaya teoriya konflikta. – M: Mayor,
2011. – 336 p .
8. Novosel'tsev V.I., Orlova D.E. Koordinatsionnoe upravlenie kak sposob
razresheniya ekonomicheskikh konfliktov / Aktual'nye problemy
innovatsionnykh sistem informatizatsii i bezopasnosti / Mater.
mezhdunarodnoy nauchno-prakticheskoy konf. – Voronezh, VIVT, 2014, pp.
434-436.
9. Novosel'tsev V.I., Orlova D.E. Osobennosti upravleniya aktivnoy
ierarkhicheskoy sistemoy s nechetko zadannymi kriteriyami / Mater. vseross.
nauchno-tekhnicheskoy konf., posvyashchennoy 95-letiyu voysk svyazi –
VUNTs VVS «VVA im. Zhukovskogo i Gagarina», Voronezh, 2014. pp.
256-260.
10. Petrov A.E. Tenzornaya metodologiya v teorii sistem. – M.: Radio i svyaz',
1985. – 152 p.
Orlova Darya Evgenievna
Email: victor_novo@mail.ru
Voronezh institute of the Federal Penitentiary Service of Russia
Voronezh, Russian Federation
