DOI
10.34229/KCA2522-9664.26.4.8
UDC 517.977
A.O. Chikrii
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine, 
g.chikrii@gmail.com
V.I. Vyshenskyy
V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine,
Kyiv, Ukraine, vyshenskyy@ukr.net
COMPARISON OF METHODS FOR INTERCEPTING CONTROLLED
TARGETS IN GAME PROBLEMS
Abstract. This study examines classical approaches to the pursuit of controlled targets in game problems. Particular attention is given to the method of resolving functions, which provides a rigorous theoretical foundation for parallel pursuit, Euler’s pursuit curve, and proportional navigation strategies. In addition, a control law implementing the beam pursuit method is proposed. Numerical simulations are conducted to model pursuit dynamics under diverse evader behaviors. Examples are presented where each of the considered methods demonstrates an advantage in terms of interception time, thereby underscoring the practical relevance of method selection in pursuit–evasion problems.
Keywords: parallel pursuit, Euler’s pursuit curve, proportional navigation, beam pursuit, method of resolving functions.
full text
REFERENCES
- Isaacs R. Differential games: A mathematical theory with applications to warfare and pursuit, control and optimization. New York: Wiley, 1965. 384 p.
- Pontryagin L.S. Selected works. Vol. 2. New York: Taylor & Francis, 1986. 618 p.
- Krasovskii N.N., Subbotin A.I. Game-theoretical control problems. New York: Springer, 1988. 517 р.
- Chikrii A.A. Conflict-controlled processes. Boston; London; Dordrecht: Kluwer Academ. Publ., 1997. 424 p.
- Locke A. Guidance. Princeton: D. Van Nostrand, 1955. 729 p.
- Shneydor N.A. Missile guidance and pursuit. Kinematics, dynamics and control. Cambridge: Woodhead Publishing, 1998. 276 p.
- Yanushevsky R. Modern missile guidance. Boca Raton: CRC Press, 2007. 240 p. https://doi.org/10.1201/9781420062281.
- Weintraub I., Garcia E., Pacher M. Optimal guidance strategy for the defence of a non-manoeuvrable target in 3-dimensions. IET Control Theory & Applications. 2020. Vol. 14, N 11. P. 1531–1538. https://doi.org/10.1049/iet-cta.2019.0541.
- Rahardian A.R., Nazaruddin Y.Y., Nadhira V., Bandong S. Implementation of parallel navigation and PID controller for drone swarm pursuit. IFAC-PapersOnLine. 2023. Vol. 56. P. 2513–2518. https://doi.org/10.1016/j.ifacol.2023.10.1300.
- Hodzic M., Prljaca N. Missile guidance using proportional navigation and machine learning. Journal of Engineering Research and Sciences. 2024. Vol. 3, N 3. P. 19–26. https://doi.org/10.55708/js0303003.
- Pashko S.V, Sinitsyn I.P. Optimal pursuit strategy using direction toward the target. Cybernetics and Systems Analysis. 2025. Vol. 61, N 5. P. 793–804. https://doi.org/10.1007/s10559-025-00812-9.
- Chikriy A.A., Matichin I.I. Resolving functions in parallel and pure pursuit. Journal of Automation and Information Sciences. 2003. Vol. 35, N 11. P. 1–6. https://doi.org/10.1615/JAutomatInfScien.v35.i11.10.
- Ignatenko A.P., Chikriy A.A. On substantiation of the proportional navigation method in the simple pursuit problem. Journal of Automation and Information Sciences. 2004. Vol. 36, N 1. P. 19–27. https://doi.org/10.1615/JAutomatInfScien.v36.i1.30.
- Glendinning P. The mathematics of motion camouflage. Proc. R. Soc. Lond. B Biol. Sci. 2004. Vol. 271, N 1538. P. 477–481. URL: https://www.jstor.org/stable/4142684.
- Matichin I.I., Chikriy A.A. Motion camouflage in differential games of pursuit. Journal of Automation and Information Sciences. 2005. Vol. 37, N 3. P. 1–5. https://doi.org/10.1615/10.1615/J Automat Inf Scien.v37.i3.10.
- Eaton J.W., Bateman D., Hauberg S., Wehbring R. GNU Octave version 10.3.0 manual: A high-level interactive language for numerical computations. 2025. URL: https://www.gnu.org/software/octave/doc/v10.3.0/.
