|Article title||TWO TARGETS PURSUIT-EVASION DIFFERENTIAL GAME WITH A RESTRICTION ON THE REVERSAL OF PURSUER|
|Section||SECTION II. SYSTEMS OF CONTROL AND MODELING|
|Month, Year||01, 2018 @en|
|Abstract||The differential game considered in this paper belongs to the class of differential pursuit-evasion games in which the pursuers are less than the targets. Targets usually form a coalition, so pursuers have to deal with a group target. For the game to make sense, the dynamics of pursuers in such games should allow to realize capture (approaching, etc.) of at least one target. This class is closely adjacent to the games in which, on the contrary, targets are less than pursuers. In such games, as a rule, "clumsy" pursuers catch "brisk" escapers. For a statement to be correct in these games the pursuers, usually, are supplied with "areas of capture", and when being inside them the escapers are considered to be caught. Recently, a special interest is attracted to games with three players of such types as Attacker-Target-Defender or Missile-Target-Defender, respectively, ATD or MTD. In these statements, the attacking player seeks to catch (hit) the fleeing target, while the task of the mobile defender is to catch the attacking player. In this paper, we give a statement and a solution to the problem of another interesting class of differential games, namely a pursuit-evasion games with a false target. Namely, the differential game of one pursuer against a coalition of two coherently dodging targets, one of which is false, is considered on the plane. The probabilities of target classification are given. The targets have simple movements. The pursuer has a restriction on the minimum allowable turning radius. The main criterion is the mathematical expectation of the distance to the true target of the terminal point in time that is not fixed in advance and chosen by the pursuer in the process of a pursuit. The saddle point of the game in program and positional strategies was found. Illustrative examples are given.|
|Keywords||Game of pursuit-evasion; false targets.|
|References||1. Ol'shanskiy V.K., Rubinovich E.Ya. Prosteyshie differentsial'nye igry presledovaniya sistemy iz dvukh ob"ektov [Simple differential games of pursuit the system of two objects], Avtomatika i telemekhanika [Automation and Remote Control], 1974, No. 1, pp. 24-34.
2. Abramyants T.G., Maslov E.P., Rubinovich E.Ya. Prosteyshaya differentsial'naya igra poocherednogo presledovaniya [The simplest differential game of alternate pursuit], Avtomatika i telemekhanika [Automation and Remote Control], 1980, No. 8, pp. 5-15.
3. Rubinovich E.Ya. Differentsial'naya igra presledovaniya «Lisa i zaytsy» [Differential pursuit game "Fox and hares"], Sb.: Problemy upravleniya v tekhnike, ekonomike, biologii [Collection: problems of management in engineering, Economics, biology]. Moscow: Nauka, 1981, pp. 29-37.
4. Abramyants T.G., Maslov E.P., Rubinovich E.Ya., Shevchenko I.I. Differentsial'nye igry s gruppovoy tsel'yu [Differential games with a group goal], Sb.: Problemy upravleniya dvizheniem i navigatsii [Collection: Problems of motion control and navigation]. Moscow: Mashinostroenie, 1983, No. 13, pp. 157-173.
5. Maslov E.P., Rubinovich E.Ya. Differentsial'nye igry s gruppovoy tsel'yu na ploskosti [Differential game with group goal on a plane], Sb.: Itogi nauki i tekhniki. Ceriya: Tekhnicheskaya kibernetika [Collection: Results of science and technology. Series: technical Cybernetics]. Moscow: VINITI, 1991, Issue 32.
6. Breakwell J.V. and Hagedorn P. Point Capture of Two Evaders in Succession, Journal of Optimization Theory and Applications, 1979, Vol. 27, No. 1.
7. Ivanov M.N. O dvukh metodakh presledovaniya v igre s terminal'noy platoy [About two methods of prosecution in the game with a terminal Board], Sb.: Upravlenie v slozhnykh nelineynykh sistemakh [Collection: Control in complex nonlinear systems]. Moscow: Nauka, 1984, pp. 30-34.
8. Ayzeks R. Differentsial'nye igry [Differential game]. Moscow: Mir, 1967, 480 p.
9. Letov A.M. Dinamika poleta i upravlenie [Flight dynamics and control]. Moscow: Nauka, 1969, 359 p.
10. Bryson A.E., Ho Yu-Chi. Applied optimal control. Toronto, London: Blaisdell Publishing Company, 1969, 544 p.
11. Zheleznov V.S., Kryakovskiy B.S., Maslov E.P. Ob odnoy zadache perekhvata [On a single interception problem], Avtomatika i telemekhanika [Automation and Remote Control], 1996, No. 8, pp. 14-21.
12. Eloy Garcia, David W Casbeer, Khanh Pham, and Meir Pachter. Cooperative aircraft defense from an attacking missile, In Decision and Control (CDC), 2014. IEEE 53rd Annual Conference on, pp. 2926-2931.
13. Meir Pachter, Eloy Garcia, and David W Casbeer. Active target defense differential game, In Communication, Control, and Computing (Allerton), 2014. 52nd Annual Allerton Conference on. IEEE, 2014, pp. 46-53.
14. Andrey Perelman, Tal Shima, and Ilan Rusnak. Cooperative differential games strategies for active aircraft protection from a homing missile, Journal of Guidance, Control, and Dynamics, 2011, Vol. 34 (3), pp. 761-773.
15. Rusnak H. Weiss, and Hexner G. Guidance laws in target-missile-defender scenario with an aggressive defender, Proceedings of the 18th IFAC World Congress, Milano, Italy, 2011.
16. Rusnak Ilan. The lady, the bandits and the body-guards - a two team dynamic game, In Proceedings of the 16th IFAC World Congress, Prague, Czech Republic, 2005.
17. Shima T. Optimal cooperative pursuit and evasion strategies against a homing missile, AIAA Journal of Guidance, Control, and Dynamics, 2011, Vol. 34 (2), pp. 414-425.
18. Takeshi Yamasaki and Sivasubramanya N Balakrishnan. Terminal intercept guidance and autopilot for aircraft defense against an attacking missile via 3d sliding mode approach, In American Control Conference (ACC), 2012. IEEE, 2012, pp. 4631-4636.
19. Takeshi Yamasaki, SN Balakrishnan, and Hiroyuki Takano. Modified command to line-of-sight intercept guidance for aircraft defense, Journal of Guidance, Control, and Dynamics, 2013, Vol. 36 (3), pp. 898-902.
20. Yanfang Liu, Naiming Qi, and Jinjun Shan. Cooperative interception with doubleline-of-sight-measuring, In AIAA Guidance, Navigation, and Control (GNC) Conference, Guidance, Navigation, and Control and Co-located Conferences. American Institute of Aeronautics and Astronautics, August 2013.