The problem of trajectories avoiding from rarefied terminal sets

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

The problem of trajectories avoiding in nonlinear conflict-controlled processes (differential games) in L.S. Pontrjagin and E.F. Mishchenko statement is considered. Terminal sets have a particular rarefied structure. Unlike other works, they consist of countable points and may have a limit points. New sufficient conditions and evasion methods are obtained, which make it possible to solve a number of avoiding trajectory problems of oscillatory systems, including the swinging problem of the generalized mathematical pendulum.

Full Text

Restricted Access

About the authors

L. P. Yugay

Uzbek State University of Physical Culture and Sport

Author for correspondence.
Email: yugailp@mail.ru
Uzbekistan, Chirchik

References

  1. Pontrjagin L.S. Selected Proceedings. Moscow: MAKS Press, 2004. 552 p. (in Russian)
  2. Isaacs R. Differential Games. N.Y.: Wiley, 1965.
  3. Krasovskii N.N., Subbotin A.I. Positional Differential Games. Moscow: Nauka, 1974. 496 p.
  4. Mishchenko E.F., Nikolskii M.S., Satimov N. The problem of avoiding encounter in several person differential games// Proc. Steklov Inst. of Math., 1977, iss. 143, pp. 105–128. (in Russian)
  5. Mishchenko E.F., Satimov N. The problem of avoiding encounter in differential games with nonlinear controls // Diff. Eqns., 1973, vol. 9, no. 10, pp. 1792–1797. (in Russian)
  6. Chernousko F.L., Akulenko L.D., Sokolov B.N. Control of Oscillations. Moscow: Nauka, 1980. 484 p. (in Russian)
  7. Reshmin S.A., Chernousko F.L. Properties of the time-optimal feedback control for a pendulum-like system // JOTA, 2014, vol.163, no. 1, pp. 230–252.
  8. Pilipenko Yu.V., Chikrii A.A. The oscillatory conflict controlled processes // JAMM, 1993, vol. 57, iss. 3, pp. 3–14. (in Russian)
  9. Bolotnik N.N., Nunuparov A.M., Chashchukhin V.G. Capsule-type vibration-driven robot an electromagnetic actuator and an opposing spring: dynamics and control of motion // J. Comput.&Syst. Sci. Int., 2016, vol. 55, no. 6, pp. 986–1000.
  10. Gusyatnikov P.B., Yugay L.P. On an evasion problem in nonlinear differential games with terminal set of compound structure// Izv. AN SSSR Techn. Kibern., 1977, no. 2, pp. 8–13. (in Russian)
  11. Mamadaliev N. On an one pursuit problem with integral restrictions on control of players // Sib. Math. J., 2015, vol. 56, no. 1, pp. 129–148. (in Russian)
  12. Yugay L.P. The problem of trajectories avoiding from rarefied terminal set // Dokl. Math., Inform., Control Proc., 2020, vol. 495,pp. 80–84. doi: 10.31857/S268695432006020X
  13. Yugay L.P. Nonlinear integral inequalities and differential games of avoiding encounter // in: Recent Developments in Automatic Control Systems. Alsbergvej: River Pub., 2022, pp. 97–111.
  14. Leihtweis K. Convex Sets. Moscow: Nauka, 1985. 336 p. (in Russian)
  15. Polovinkin E.S. Multi-Valued Analysis and Differential Inclusions. Moscow: Fizmatlit, 2014. 524 p. (in Russian)
  16. Kurzhanskii A.B. Control and Observation under Uncertainty. Moscow: Nauka, 1977. 392 p. (in Russian)
  17. Subbotin A.I., Chentsov A.G. Optimization of Guarantee in Control Problems. Moscow: Nauka, 1981. 288 p. (in Russian)

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2024 Russian Academy of Sciences