Skip to main content

Pursuit-Evasion Differential Games Applied to a 3-Dimensional Missile Guidance Problem Using the Liapunov Approach

  • Chapter
Mechanics and Control

Abstract

In this paper we shall outline a technique using Liapunov functions and sufficiency conditions to estimate the winning region for a three-phase missile entering its coast phase. We shall use point-mass dynamics with variable mass to model the missile trajectories in three dimensions. We will then use this estimated winning region to provide a procedure whereby we can judge the robustness of a particular three dimensional guidance law when one or more of its parameters has bounds imposed upon it. This technique effectively establishes a benchmark against which guidance laws with different bounds upon their parameters can be compared. We shall then give an example using a pursuit-evasion scenario between an AMRAAM AIM-120A missile and a F-15E “Strike Eagle” fighter.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.M. Anderson, “Comparison of Optimal Control and Differential Game Intercept Missile Guidance Laws”, J. Guidance, Control and Dynamics Vol. 4, No. 2, 1981.

    Google Scholar 

  2. A. Blaquière, Gérard, and G. Leitmann, Qualitative and Quantitative Differential Games Academic Press, 1975.

    Google Scholar 

  3. M.H. Breitner, H.J. Pesch, and W. Grimm, Complex Differential Games of Pursuit-Evasion Type with State Constraint, Part 1: Necessary Conditions for Optimal Open-Loop Strategies; Part 2: Numerical Computation of Optimal Open-Loop Strategies. Mathematisches Institute, Technische Universität München, Reports 314/315, 1992.

    Google Scholar 

  4. A.E. Bryson and Y.C. Ho, Applied Optimal Control Hemisphere Publishing Corp., Washington DC, 1975.

    Google Scholar 

  5. A. Davidovitz, J. Shinar, “Eccentric Two-Target Model for Qualitative Air-Combat Game Analysis”, J. Guidance, Control and Dynamics, Vol. 8, No. 3, 1985.

    Google Scholar 

  6. P. Garnell, Guided Weapon Control Systems (Second Edition), Pergamon Press, 1980.

    Google Scholar 

  7. W.M. Getz and G. Leitmann, “Qualitative Differential Games with Two Targets”, Journal of Mathematical Analysis and Applications vol. 68(2), 1979, pp.421–430.

    Article  MathSciNet  MATH  Google Scholar 

  8. W.M. Getz and M. Pachter, “Two-Target Pursuit-Evasion Differential Games in the Plane”, JOTA Vol. 34, No. 3, pp. 383–403, July 1981.

    Article  MathSciNet  MATH  Google Scholar 

  9. N.J.C. Greenwood, “A Differential Game in Three Dimensions: The Aerial Dogfight Scenario”, J.Dynamics and Control vol. 2(2), pp.161–200, 1992.

    Article  MathSciNet  MATH  Google Scholar 

  10. M. Guelman, “A Qualitative Study of Proportional Navigation”, IEEE Transactions on Aerospace and Electronic Systems, Vol. AES-7, No. 4, pp. 637–643, 1972.

    Article  MathSciNet  Google Scholar 

  11. M. Guelman, J. Shinar, and A. Green, “Qualitative Study ofa Planar Pursuit Evasion Game in the Atmosphere”, Proc. of AIAA Guidance, Navigation and Control Conference Paper No. 88–4158-CP, Minneapolis, Minnesota, 1988.

    Google Scholar 

  12. W. Herbst, “Dynamics of Air Combat”, Journal of Aircraft Vol. 20, pp. 594–598, 1983.

    Article  Google Scholar 

  13. R. Isaacs, Differential Games John Wiley and Sons, New York 1965.

    MATH  Google Scholar 

  14. B. Järmark, “A Missile Duel Between Two Aircraft”, J. Guidance, Control, and Dynamics Vil. 8, No. 3, 1985, pp. 508–513.

    Google Scholar 

  15. P.K.A. Menon and E.L. Duke “Time-Optimal Pursuit-Evasion with a Weapon Envelope Constraint”, Proc. of the 1990 American Control Conference San Diego, pp. 2337–2342, 1990.

    Google Scholar 

  16. A.W. Merz, “To Pursue or to Evade - That is the Question”, J. Guidance, Control and Dynamics, Vol 8, No 2, pp. 161–166, 1985.

    Article  MathSciNet  MATH  Google Scholar 

  17. K. Moritz, R. Polis, and K.H. Well, “Pursuit-Evasion in Medium-Range Air- Combat Scenarios”, Comp. Math. Applic., Vol. 13, No. 1–3, pp 167–180, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  18. M. Pachter and W.M. Getz, “The Geometry of the Barrier in the Game of Two Cars”, Optimal Control Applications and Methods, Vol. 1, pp. 103–118, 1980.

    Article  MathSciNet  MATH  Google Scholar 

  19. R.A. Poulter and G.M. Anderson, “A Guidance Concept for Air-to-Air Missiles Based on Nonlinear Differential Game Theory”, Proc. NAECON, pp. 605–609, 1976.

    Google Scholar 

  20. J. Shinar, and S. Gazit, “Optimal No-Escape Envelopes of Guided Missiles”, Proc. of AIAA Guidance, Navigation and Control Conference Paper 85–1960, Snowmass, Colorado, 1985.

    Google Scholar 

  21. J. Shinar and S. Gutman, “Three-dimensional Optimal Pursuit and Evasion with Bounded Control”, IEEE Trans. on Automatic Control, Vol AC-25, pp. 492–496, 1980.

    Article  MathSciNet  Google Scholar 

  22. J.M. Skowronski, “The Barrier in a Pursuit-Evasion Game with Two Targets”, Comput. Math. Applic., vol. 13(1–3), pp.37–45, 1987.

    Article  MathSciNet  MATH  Google Scholar 

  23. J.M. Skowronski, “Winning Controllers for Nonlinear Air Combat Game with Reduced Dynamics”, Proc. AIAA Guidance, Navigation and Control Conference Minneapolis, pp.866–873, 1988.

    Google Scholar 

  24. J.M. Skowronski and R.J. Stonier, “Two-Person Qualitative Differential Games with Two Objectives”, Computers Math. Applic., vol 18(1–3), Pergamon Press 1989, 133–150.

    Article  MathSciNet  MATH  Google Scholar 

  25. R. De Villiers, C.J. Wright and Y. Yavin, “A Stochastic Pursuit-Evasion Differential Game in 3-D: Optimal Evasion Strategies”, Comp. Math. Applic., Vol. 13, No. 7, pp. 623–630, 1987

    Article  Google Scholar 

  26. P.-J. Yuan and J.-S. Chern, “Ideal Proportional Navigation”, J. Guidance, Control and Dynamics, Vol. 15, No. 5, 1992.

    Google Scholar 

  27. P.-J. Yuan and J.-S. Chern, “Solutions of True Proportional Navigation for Manuevering and Nonmanuevering Targets”, J. Guidance, Control and Dynamics Vol. 15, No. 1, pp. 268–271, 1992.

    Article  Google Scholar 

  28. P. Zarchan, “Tactical and Strategic Missile Guidance”, Progress in Astronautics and Aeronautics, Vol 124, AIAA Tactical Missile Series, Washington DC, 1990.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer Science+Business Media New York

About this chapter

Cite this chapter

Greenwood, N.J.C. (1994). Pursuit-Evasion Differential Games Applied to a 3-Dimensional Missile Guidance Problem Using the Liapunov Approach. In: Guttalu, R.S. (eds) Mechanics and Control. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2425-0_10

Download citation

  • DOI: https://doi.org/10.1007/978-1-4615-2425-0_10

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6029-2

  • Online ISBN: 978-1-4615-2425-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics