Cybernetics And Systems Analysis logo
Editorial Board Announcements Abstracts Authors Archive
KIBERNETYKA TA SYSTEMNYI ANALIZ
International Theoretical Science Journal
Volume 60 >>> № 2 MARCH — APRIL 2024
-->

DOI 10.34229/KCA2522-9664.24.2.8
UDC 517.977
A.A Chikrii1, I.S. Rappoport2


1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

 g.chikrii@gmail.com

2 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

 jeffrappoport@gmail.com

CONTROL STRATEGIES IN THE PROBLEM OF APPROACH
OF CONFLICT-CONTROLLED OBJECTS

Abstract. The authors propose a new approach to forming control strategies in the problem of approach of conflict-controlled objects. Modifications of the first direct method is developed for the stroboscopic strategy in the class of counter-controls where the classical Pontryagin’s condition is not satisfied. The lower resolving function is considered, which plays a key role in the formulation of the results and in the general case can be determined using the Minkowski functional of a multivalued mapping. An upper resolving function is introduced and a modified scheme of the method of resolving functions is proposed, which guarantees the termination of the conflict-controlled process in the class of quasi-strategies and counter-controls where the classical Pontryagin’s condition is not satisfied. The guaranteed times for different schemes of the considered methods are compared. The theoretical results are illustrated on a second-order model example with a special non-convex control region of the pursuer.

Keywords: control strategy, resolving function, dynamic game problem, problem of approach of controlled objects.


full text

REFERENCES

  1. Pontryagin L.S. Selected scientific works [in Russian]. Vol. 2. Moscow: Nauka, 1988. 576 p.

  2. Chikrii A.A. Conflict controlled processes. Boston; London; Dordrecht: Springer Science and Business Media, 2013. 424 p.

  3. Chikrii A.O., Rappoport Y.S. Modifications of the Pontryagin condition in the problem of convergence of conflict-controlled objects. Kibernetyka ta systemnyi analiz. 2022. Vol. 58, N 6. P. 95–105. https://doi.org/10.1007/s10559-023-00527-9.

  4. Chikrii A.A., Chikrii V.K. Image structure of multivalued mappings in game problems of motion control. Journal of Automation and Information Sciences. 2016. Vol. 48, N 3. P. 20–35.

  5. Chikrii A.O., Rappoport Y.S. A direct method of solving game problems of convergence of controlled objects. Kibernetyka ta systemnyi analiz. 2023. Vol. 59, N 5. P. 144–153. https://doi.org/10.1007/s10559-023-00617-8.

  6. Pshenichnyi B.N., Ostapenko V.V. Differential games [in Russian]. Kyiv: Nauk. dumka, 1992. 263 p.

  7. Nikolsky M.S. The first direct method of L.S. Pontryagin in differential games [in Russian]. Moscow: Moscow State University Publishing House, 1984. 65 p.

  8. Hajek O. Pursuit games. Vol. 12. New York: Acad. Press. 1975. 266 p.

  9. Aubin J.-P., Frankowska H. Set-valued analysis. Boston; Basel; Berlin: Birkhauser, 1990. 461 p.

  10. Rockafellar R. Convex analysis [Russian translation]. Moscow: Mir, 1973. 470 p.

  11. Pshenichny B.N. Convex analysis and extremal problems [in Russian]. Moscow: Nauka, 1980. 320 p.

  12. Chikrii A.A., Rappoport I.S. Method of resolving functions in the theory of conflict-controlled processes. Kibernetika i sistemnyj analiz. 2012. Vol. 48, N 5. P. 40–64.

  13. Patsko V., Quincampoix M. Preface: DGAA special issue on pursuit-evasion games and differential games with incomplete information. Dyn. games. Vol. 12. Appl 9. P. 569–572. https://doi.org/10.1007/s13235-019-00312-4.

  14. Patsko V., Kumkov S., Turova V. Pursuit-evasion games. Basar T., Zaccour G. (eds.). Handbook of dynamic game theory. Cham: Springer, 2018. https://doi.org/10.1007/978-3-319- 44374-4_30.

  15. Silveira J., Cabral K., Rabbath C.-A., Givigi S. Deep reinforcement learning solution of reach-avoid games with superior evader in the context of unmanned aerial systems. International conference on unmanned aircraft systems (ICUAS). Warsaw, Poland, 2023. P. 911–918. https://doi.org/10.1109/ICUAS57906.2023.10156154.

  16. Luo Y., Jiang X., Zhong S., Ji Y., Sun G. A multi-satellite swarm pursuit-evasion game based on contract network protocol and optimal lambert method. Yan L., Duan H., Deng Y. (eds.). Advances in Guidance, Navigation and Control. ICGNC 2022. Lecture Notes in Electrical Engineering. Singapore: Springer. 2022. Vol. 845. https://doi.org/10.1007/978-981-19-6613-2_222.

  17. Lee Y., Bakolas E., Akellab M.R. Feedback strategies for hypersonic pursuit of a ground evader. IEEE Aerospace Conference (AERO). Big Sky, MT, USA, 2022. P. 1–7. https://doi.org/10.1109/AERO53065.2022.9843434.

  18. Xiao Liang, Boran Zhou, Linping Jiang, Guanglei Meng, Yiwei Xiu. Collaborative pursuit-evasion game of multi-UAVs based on Apollonius circle in the environment with obstacle. Connection Science. 2023. Vol. 35, N 1. https://doi.org/10.1080/09540091.2023. 2168253.

  19. Tan M., Shen H. The differential game cooperative guidance law for the single target. Yan L., Duan H., Deng Y. (eds.). Advances in Guidance, Navigation and Control. ICGNC. Lecture Notes in Electrical Engineering. Singapore: Springer. 2022. Vol. 845. https://doi.org/10.1007/978-981-19-6613-2_188.




Editorial Board Announcements Abstracts Authors Archive
about scope office editorial board instructions for authors subscriptions contacts
© 2024 Kibernetika.org. All rights reserved.