Method of constructing and estimating asymptotic controllability sets of two-dimensional linear discrete systems with limited control

DOI: 10.34759/trd-2022-126-17

Аuthors

Ibragimov D. N.^*, Berendakova A. V.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: rikk.dan@gmail.com
**e-mail: abv1998@yandex.ru

Keywords:

two-dimensional discrete controlling system, set of controllability, bounded polyhedron, convex polyhedron, convex compact set

References

1. Sirotin A.N., Formal’skii A.M. Avtomatika i telemekhanika, 2003, no. 12, pp. 17–32.
2. Fisher M.E., Gayek J.E. Estimating Reachable Sets for Two-Dimensional Linear Discrete Systems, Journal of Optimization Theory and Applications, 1988, vol. 56, no. 1, pp .67-88.
3. Desoer C.A., Wing J. The minimal time regulator problem for linear sampled-data systems: general theory, Journal Franklin Institute, 1961, vol. 272, no. 3, pp. 208-228.
4. Hamza M.H., Rasmy M.E. A Simple Method for Determining the Reahable Set for Linear Discrete Systems, IEEE Transactions on Automatic Control, 1971, vol. 16, pp. 281-282.
5. Kalman R. Ob obshchei teorii sistem upravleniya, Trudy I Mezhdunarodnogo kongressa IFAK, Moscow, Izd-vo AN SSSR, 1961, vol. 2, pp. 521-547.
6. Ibragimov D.N., Sirotin A.N. Atomatika i telemekhanika, 2015, no. 9, pp. 3-30.
7. Ibragimov D.N. Trudy MAI, 2015, no. 83. URL: https://trudymai.ru/eng/published.php?ID=62313
8. Boltyanskii V.G. Optimal’noe upravlenie diskretnymi sistemami (Optimal control of discrete-time systems), Moscow, Nauka, 1973, 448 p.
9. Pontryagin L.S., Boltyanskii V.G., Gamkrelidze R.V., Mishchenko B.F. Matematicheskaya teoriya optimal’nykh protsessov (Mathematical theory of the optimal processes), Moscow, Nauka, 1983, 393 p.
10. Ibragimov D.N. Avtomatika i telemekhanika, 2019, no. 3, pp. 3–25. DOI: 10.1134/S0005231019030012
11. Khorn R., Dzhonson Ch. Matrichnyi analiz (Matrix analysis), Мoscow, Mir, 1989, 655 p.
12. Ivanov D.S., Ovchinnikov M.Yu., Tkachev S.S. Izvestiya RAN. Teoriya o sistemy upravleniya, 2011, no. 1, pp. 107-119.
13. Kronover R.M. Fraktaly i khaos v dinamicheskikh sistemakh (Fractals and chaos in dynamic systems), Moscow, Postmarket, 2000, 352 p.
14. Moroz A.I. Avtomatika i telemekhanika, 1965, no. 2, pp. 193-207
15. Propoi A.I. Elementy teorii optimal’nykh diskretnykh protsessov (Elements of the theory of optimal discrete processes), Moscow, Nauka, 1973, 255 p.
16. Evtushenko Yu.G. Metody resheniya ekstremal’nykh zadach i ikh prilozheniya v zadachakh optimizatsii (Methods for solving extreme problems and their applications in optimization problems), Moscow, Nauka, 1982, 432 p.
17. Agrachev A.A., Sachkov Yu.L. Geometricheskaya teoriya upravleniya (Geometric theory of control), Moscow, Nauka, 2005, 391 p.
18. Orlov D.A., Saitova A.G. Trudy MAI, 2018, no. 100. URL: https://trudymai.ru/eng/published.php?ID=93375
19. Moiseev N.N. Elementy teorii optimal’nykh sistem (Elements of the theory of optimal systems), Moscow, Nauka, 1975, 526 p.
20. Sokolov N.L. Trudy MAI, 2016, no. 87. URL: https://trudymai.ru/eng/published.php?ID=69701

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