DOI
10.34229/KCA2522-9664.24.4.7
UDC 517.977
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
|
SUFFICIENT APPROACH CONDITIONS FOR CONFLICT CONTROLLED
OBJECTS WITH DIFFERENT INERTIA
Abstract. The problem of convergence of controlled objects with different inertia in dynamic game problems is considered. For controlled objects with different inertia, it is characteristic that the Pontryagin condition is not satisfied on a time interval. To solve the problem, a special multivalued mapping and a matrix function are introduced to equalize the players’ control resources, and then the additional resource is compensated by the body component of the cylindrical terminal set. With the help of the lower resolving function for objects with different inertia, two modified schemes of the first direct Pontryagin method are proposed, which guarantee the successful completion of the conflict-controlled process in the class of countercontrols. The upper resolving function is introduced and the corresponding modified schemes of the method of resolving functions for controlled objects with different inertia in the class of quasi-strategies and counter-controls are presented. New theoretical results are illustrated by a model example.
Keywords: controlled objects with different inertia, quasilinear differential game, multi-valued mapping, measurable selector, stroboscopic strategy, resolving function.
full text
REFERENCES
- Logiewa R., Hoffmann F., Govaers F., Koch W. Dynamic pursuit-evasion scenarios with a varying number of pursuers using deep sets. IEEE Symposium sensor data fusion and international conference on multisensor fusion and integration (SDF-MFI). Bonn, Germany, 2023. P. 1–7. doi.org/10.1109/SDF-MFI59545.2023.10361514 .
- Fang X., Wang C., Xie L., Chen J. Cooperative pursuit with multi-pursuer and one faster free-moving evader. IEEE Transactions on Cybernetics. 2022. Vol. 52, N 3. P. 1405–1414. doi.org/10.1109/TCYB.2019.2958548.
- Yuchen H., Hongjian W., YuDan Y.D., WangZhao W. Research on multi-UUV pursuit-evasion games strategies under the condition of strongly manoeuvrable evader. 2021. 40th Chinese Control Conference (CCC). Shanghai, China, 2021. P. 5504–5511. doi.org/10.23919/CCC52363.2021.9550358 .
- Lee Y., Bakolas E. Relay pursuit of an evader by a heterogeneous group of pursuers using potential games. American Control Conference (ACC). New Orleans, LA, USA, 2021. P. 3182–3187. doi.org/10.23919/ACC50511.2021.9482912.
- 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. doi.org/10.1109/ICUAS57906.2023.10156154 .
- 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. Vol. 845. Singapore: Springer. 2022. doi.org/10.1007/978-981-19-6613- 2_222.
- Lee Y., Bakolas E., Akella M.R. Feedback strategies for hypersonic pursuit of a ground evader. IEEE Aerospace Conference (AERO). Big Sky, MT, USA, 2022. P. 1–7. doi.org/10.1109/AERO53065.2022.9843434.
- 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. doi.org/10.1080/ 09540091.2023.2168253.
- 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 2022. Lecture Notes in Electrical Engineering. Vol. 845, 2022. Singapore: Springer. doi.org/10.1007/978-981-19-6613-2_188 .
- Chikrii A.O., Rappoport Y.S. A modified method of solving functions in game problems of convergence of controlled objects with different inertia. Kibernetyka ta systemnyi analiz. 2023. Vol. 59, N 2. P. 87–103.
- Chikrii A.O., Rappoport Y.S. A direct method of resolving game problems of convergence of controlled objects. Kibernetyka ta systemnyi analiz. 2023. Vol. 59, N 5. P. 144–153.
- 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.
- Nikolsky M.S. The first direct method of L.S. Pontryagin in differential games. Moscow: Moscow State University Publishing House, 1984. 65 p.
- Chikrii A.A. Conflict controlled processes. Boston; London; Dordrecht: Springer Science and Business Media, 2013. 424 p.
- Pshenichny B.N. Convex analysis and extremal problems. Moscow: Nauka, 1980. 320 p.
- Pshenichny B.N., Ostapenko V.V. Differential games. Kyiv: Nauk. dumka. 1992, 263 p.
- Hajek O. Pursuit games. Vol. 12. New York: Acad. Press, 1975. 266 p.
- Aubin J.-P., Frankowska H. Set-valued analysis. Boston; Basel; Berlin: Birkhauser, 1990. 461 p.
- Rockafellar R. Convex analysis. Moscow: Mir, 1973. 470 p.
- 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 4. P. 40–64.
