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On Applied Nonlinear and Bilevel Programming or Pursuit-Evasion Games

Author

Listed:
  • H. Ehtamo

    (Helsinki University of Technology)

  • T. Raivio

    (Helsinki University of Technology)

Abstract

Motivated by the benefits of discretization in optimal control problems, we consider the possibility of discretizing pursuit-evasion games. Two approaches are introduced. In the first approach, the solution of the necessary conditions of the continuous-time game is decomposed into ordinary optimal control problems that can be solved using discretization and nonlinear programming techniques. In the second approach, the game is discretized and transformed into a bilevel programming problem, which is solved using a first-order feasible direction method. Although the starting points of the approaches are different, they lead in practice to the same solution algorithm. We demonstrate the usability of the discretization by solving some open-loop representations of feedback solutions for a complex pursuit-evasion game between a realistically modeled aircraft and a missile, with terminal time as the payoff. The solutions are compared with those obtained via an indirect method.

Suggested Citation

  • H. Ehtamo & T. Raivio, 2001. "On Applied Nonlinear and Bilevel Programming or Pursuit-Evasion Games," Journal of Optimization Theory and Applications, Springer, vol. 108(1), pages 65-96, January.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:1:d:10.1023_a:1026461805159
    DOI: 10.1023/A:1026461805159
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    Cited by:

    1. Yu Wang & Xiangtong Qi, 2017. "Evasion policies for a vessel being chased by pirate skiffs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 64(6), pages 453-475, September.
    2. Matthew W. Harris, 2020. "Abnormal and Singular Solutions in the Target Guarding Problem with Dynamics," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 627-643, February.

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