Log in

Pursuit in the Presence of a Defender

  • Published:
Dynamic Games and Applications Aims and scope Submit manuscript

Abstract

A zero-sum pursuit-evasion differential game with three players, a Target, an Attacker, and a Defender, is considered. The Attacker pursues the Target aircraft, while the Defender strives to intercept the Attacker before he reaches the aircraft. In this paper, the game in the state space region where the Attacker prevails is analyzed. The state space region where the Target is vulnerable is characterized and the Attacker’s strategy for capturing the Target despite the presence of the Defender is derived. The players’ optimal strategies mesh with the previously obtained strategies in the state space region where the Active Target Defense Differential Game is played, and the Defender’s presence by virtue of him intercepting the Attacker allows the Target to escape.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Ardema MD, Heymann M, Rajan N (1985) Combat games. J Optim Theory Appl 46(4):391–398

    Article  MathSciNet  MATH  Google Scholar 

  2. Bakolas E, Tsiotras P (2010) Optimal pursuit of moving targets using dynamic Voronoi diagrams. In: 49th IEEE conference on decision and control, pp 7431–7436

  3. Breakwell JV, Hagedorn P (1979) Point capture of two evaders in succession. J Optim Theory Appl 27(1):89–97

    Article  MathSciNet  MATH  Google Scholar 

  4. Chen M, Zhou Z, Tomlin CJ (2017) Multiplayer reach-avoid games via pairwise outcomes. IEEE Trans Autom Control 62(3):1451–1457

    Article  MathSciNet  MATH  Google Scholar 

  5. Garcia E, Casbeer DW, Pachter M (2015) Cooperative strategies for optimal aircraft defense from an attacking missile. J Guid Control Dyn 38(8):1510–1520

    Article  Google Scholar 

  6. Garcia E, Casbeer DW, Pachter M (2017) Active target defense using first order missile models. Automatica 78:139–143

    Article  MathSciNet  MATH  Google Scholar 

  7. Getz WM, Leitmann G (1979) Qualitative differential games with two targets. J Math Anal Appl 68(2):421–430

    Article  MathSciNet  MATH  Google Scholar 

  8. Getz WM, Pachter M (1981) Capturability in a two-target game of two cars. J Guid Control Dyn 4(1):15–21

    Article  MATH  Google Scholar 

  9. Isaacs R (1951) Games of pursuit. Paper P-257. RAND Corporation, Santa Monica

  10. Isaacs R (1965) Differential games. Wiley, New York

    MATH  Google Scholar 

  11. Liu SY, Zhou Z, Tomlin C, Hedrick K (2013) Evasion as a team against a faster pursuer. In: American control conference, pp 5368–5373

  12. Olshanskii VK, Rubinovich EY (1974) Elementary differential games of pursuit of a two-object system. Autom Remote Control 35(1):19–28

    MathSciNet  Google Scholar 

  13. Oyler DW, Kabamba PT, Girard AR (2016) Pursuit-evasion games in the presence of obstacles. Automatica 65:1–11

    Article  MathSciNet  MATH  Google Scholar 

  14. Pachter M, Garcia E, Casbeer DW (2014) Active target defense differential game. In: 52nd annual Allerton conference on communication, control, and computing, pp 46–53

  15. Pachter M, Garcia E, Casbeer DW (2018) Toward a solution of the active target defense differential game. Dyn Games Appl. https://doi.org/10.1007/s13235-018-0250-1

  16. Robb M, Tsourdos A, White BA (2006) Earliest intercept line guidance using a game theory approach. In: AIAA guidance, navigation, and control conference and exhibit

  17. Rubinsky S, Gutman S (2014) Three-player pursuit and evasion conflict. J Guid Control Dyn 37(1):98–110

    Article  Google Scholar 

  18. Rusnak I, Weiss H, Hexner G (2011) Guidance laws in target-missile-defender scenario with an aggressive defender. In: Proceedings of the 18th IFAC world congress, pp 9349–9354

  19. Scott W, Leonard NE (2013) Pursuit, herding and evasion: a three-agent model of caribou predation. In: American control conference, pp 2978–2983

  20. Selvakumar J, Bakolas E (2017) Evasion with terminal constraints from a group of pursuers using a matrix game formulation. In: American control conference, pp 1604–1609

  21. Shalumov V, Shima T (2017) Weapon-target-allocation strategies in multiagent target-missile-defender engagement. J Guid Control Dyn 40(10):2452–2464

    Article  Google Scholar 

  22. Weiss M, Shima T, Castaneda D, Rusnak I (2017) Combined and cooperative minimum-effort guidance algorithms in an active aircraft defense scenario. J Guid Control Dyn 40(5):1241–1254

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Eloy Garcia.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Garcia, E., Casbeer, D.W. & Pachter, M. Pursuit in the Presence of a Defender. Dyn Games Appl 9, 652–670 (2019). https://doi.org/10.1007/s13235-018-0271-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13235-018-0271-9

Keywords

Navigation