Journal of Optimization Theory and Applications

, Volume 78, Issue 3, pp 419–441 | Cite as

Complex differential games of pursuit-evasion type with state constraints, part 1: Necessary conditions for optimal open-loop strategies

  • M. H. Breitner
  • H. J. Pesch
  • W. Grimm
Contributed Papers


Complex pursuit-evasion games with state variable inequality constraints are investigated. Necessary conditions of the first and the second order for optimal trajectories are developed, which enable the calculation of optimal open-loop strategies. The necessary conditions on singular surfaces induced by state constraints and non-smooth data are discussed in detail. These conditions lead to multi-point boundary-value problems which can be solved very efficiently and very accurately by the multiple shooting method. A realistically modelled pursuit-evasion problem for one air-to-air missile versus one high performance aircraft in a vertical plane serves as an example. For this pursuit-evasion game, the barrier surface is investigated, which determines the firing range of the missile. The numerical method for solving this problem and extensive numerical results will be presented and discussed in Part 2 of this paper; see Ref. 1.

Key Words

Differential games pursuit-evasion games singular surfaces barrier surface state constraints open-loop strategies multipoint boundary-value problems flight mechanics missile firing range 


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Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • M. H. Breitner
    • 1
  • H. J. Pesch
    • 1
  • W. Grimm
    • 2
  1. 1.Department of MathematicsUniversity of TechnologyMunichGermany
  2. 2.Department of Flight Mechanics and ControlUniversity of StuttgartStuttgartGermany

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