Modelling and Data Analysis

2021. Vol. 11, no. 1, 20–32

doi:10.17759/mda.2021110102

ISSN: 2219-3758 / 2311-9454 (online)

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

## Abstract

## General Information

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

**Journal rubric:** Control Theory

**DOI:** https://doi.org/10.17759/mda.2021110102

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

**For citation:**
Ibragimov D.N., Novozhilkin N.M. On a Method for Constructing a Linear Nonstationary Discrete System with Full-Dimensional Controlby Changing the Quantization Step. *Modelirovanie i analiz dannikh = Modelling and Data Analysis,* 2021. Vol. 11, no. 1, pp. 20–32. DOI: 10.17759/mda.2021110102. (In Russ., аbstr. in Engl.)

## References

- Sirotin А.N. Controllability of linear discrete systems with bounded control and (almost) periodicdisturbances // Аutomatica and telemechanica. 2001. No.5. P. 53–64.
- 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.
- Rokafellar Р. Convex Analysis.// Мir, 1973.
- Ibragimov D.N. Speed-optimal satellite orbit correction // Electron.Trudy. МAI. 2017. No. 94.
- 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.
- Кolmogorov А.N., Fomin S.V. Elements of function theory and functional analysis. Fizmalit, 2012.
- Danford N., Shvartz Dj. V. Linear operators. V. 2. Spectral theory. Self-adjoint operators in a Hilbert space//Mir, 1966.
- Мalishev V.V., Кibzun А.I. Analysis and synthesis of high-precision control of aircraft.// Mashinostroenie, 1987.
- Мalishev V.V., Кrasilchikov M.N., Bobronnikov V.Т and other. Satellite monitoring systems. // МAI, 2000.
- Pontryagin L.S.,Boltyansky V.G., Gamkrelidze R.V., Мischenko B.F. Mathematical theory of optimal processes. // Nauka, 1969.
- Boltyansky V.G. Optimal control mathematical methods. // Nauka, 1969.
- Мoiseev N.N. Elements of the theory of optimal systems. // Nauka, 1975.
- Evtushenko Y.G. Methods for solving extreme problems and their applications in optimization systems. // Nauka, 1982.
- Boltyansky V.G. Optimal control of discrete systems. //Nauka, 1973.
- Propoi А.I. Elements of the theory of optimal discrete processes. // Nauka, 1973.
- 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.
- Bellman R. Dynamic programming. // IIL, 1960.
- 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.
- 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.

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