Russian Psychological Issues
JournalsTopicsAuthorsEditor's Choice For AuthorsAbout PsyJournals.ruContact Us

Previous issue (2021. Vol. 11, no. 1)

Modelling and Data Analysis

Publisher: Moscow State University of Psychology and Education

ISSN (printed version): 2219-3758

ISSN (online): 2311-9454


License: CC BY-NC 4.0

Started in 2011

Published 4 times a year

Free of fees
Open Access Journal


On a Method for Constructing a Linear Nonstationary Discrete System with Full-Dimensional Controlby Changing the Quantization Step 23


Ibragimov D.N.
PhD in Physics and Matematics, Senior Lecturer, Moscow Aviation Institute (National Research University), Moscow, Russia

Novozhilkin N.M.
Moscow, Russia

The method that allows one to reduce a stationary system with control of incomplete dimension to a non-stationary periodic system with control of full dimension is considered in this article. The paper proves the equivalence of these systems, and also that the optimal in terms of speed for a non-stationary system is also optimal for the original stationary system. A satellite attitude control system is considered as an example.

Keywords: linear discrete-time control system, performance problem, set of controllability.

Column: Control Theory


For Reference


The work was carried out with the financial support of the RFBR grant No. 18–08–00128-a.

  1. Sirotin А.N. Controllability of linear discrete systems with bounded control and (almost) periodicdisturbances // Аutomatica and telemechanica. 2001. No.5. P. 53–64.
  2. Кostousova E.K. External polyhedral estimation of reachable sets in an “extended” space for linear multistage systems with integral constraints on control //Vichislitelnye Technologii. 2004. V 9. No. 4. P. 54–72.
  3. Rokafellar Р. Convex Analysis.// Мir, 1973.
  4. Ibragimov D.N. Speed-optimal satellite orbit correction // Electron.Trudy. МAI. 2017. No. 94.
  5. Ibragimov D.N. On the speed problem for a class of linear autonomous infinite-dimensional systems with discrete time, bounded control, and a degenerate operator // Аutomatica and telemechanica. 2019. No. 2. P. 32–59.
  6. Кolmogorov А.N., Fomin S.V. Elements of function theory and functional analysis. Fizmalit, 2012.
  7. Danford N., Shvartz Dj. V. Linear operators. V. 2. Spectral theory. Self-adjoint operators in a Hilbert space//Mir, 1966.
  8. Мalishev V.V., Кibzun А.I. Analysis and synthesis of high-precision control of aircraft.// Mashinostroenie, 1987.
  9. Мalishev V.V., Кrasilchikov M.N., Bobronnikov V.Т and other. Satellite monitoring systems. // МAI, 2000.
  10. Pontryagin L.S.,Boltyansky V.G., Gamkrelidze R.V., Мischenko B.F. Mathematical theory of optimal processes. // Nauka, 1969.
  11. Boltyansky V.G. Optimal control mathematical methods. // Nauka, 1969.
  12. Мoiseev N.N. Elements of the theory of optimal systems. // Nauka, 1975.
  13. Evtushenko Y.G. Methods for solving extreme problems and their applications in optimization systems. // Nauka, 1982.
  14. Boltyansky V.G. Optimal control of discrete systems. //Nauka, 1973.
  15. Propoi А.I. Elements of the theory of optimal discrete processes. // Nauka, 1973.
  16. Holtzman J.M., Halkin H. Directional Convexity and the Maximum Principle for Discrete Systems // J. SIAM Control. V. 4. No. 2. 1966. P. 263–275.
  17. Bellman R. Dynamic programming. // IIL, 1960.
  18. Ibragimov D.N., Sirotin А.N. On the speed problem for a class of linear autonomous infinite dimensional systems with discrete time and bounded control. // Аutomatica and telemechanica. 2017. No. 10. P. 3–32.
  19. Sirotin А.N., Formalsky А.М. Achievability and controllability of discrete systems with limited in magnitude and impulse control actions // Аutomatica and telemechanica. 2003. No. 12. P. 17–32.

© 2007–2021 Portal of Russian Psychological Publications. All rights reserved in Russian

Publisher: Moscow State University of Psychology and Education

Catalogue of academic journals in psychology & education MSUPE

Creative Commons License Open Access Repository     Webometrics Ranking of Repositories

RSS Psyjournals at facebook Psyjournals at Twitter Psyjournals at Youtube ??????.???????