On Optimal Missile Guidance Upgrades with Dynamic Stackelberg Game Linearizations

  • Michael H. Breitner
  • Uwe Rettig
  • Oskar von Stryk
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 6)


We investigate the most critical final homing phase for one intercepting missile versus one maneuverable ballistic missile. In the worst case a future ballistic missile will know the intercepting missile’s guidance scheme and could maximize the minimum (miss) distance. An intercepting missile with three-dimensional proportional navigation guidance is studied. An optimal small guidance upgrade for this missile is calculated as a closed-loop solution of a dynamic Stackelberg game. The intercepting missile acts as leader, whereas the ballistic missile advantageously acts as follower. An optimal small upgrade is approximated numerically along very many optimal trajectories that cover the relevant final homing scenarios. The trajectories are computed efficiently by a direct collocation method. Along the trajectories a linearized minimum—maximum principle using the adjoint variables’ estimates is applied. An upgrade with nearest points on neighboring optimal trajectories is synthesized. Alternative synthesis approaches with local Taylor-series expansions with global smoothing or with artificial neural networks are discussed. Simulations for many different scenarios show the improved interception capability for the upgraded guidance of the intercepting missile.


Optimal Control Problem Differential Game Ballistic Missile Guidance Scheme Evasive Maneuver 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Michael H. Breitner
    • 1
  • Uwe Rettig
    • 2
  • Oskar von Stryk
    • 2
  1. 1.Fachbereich Mathematik und InformatikTechnische Universität ClausthalClausthal-ZellerfeldGermany
  2. 2. Zentrum Mathematik MünchenTechnische UniversitätMünchenGermany

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