Journal of Optimization Theory and Applications

, Volume 33, Issue 3, pp 401–418

Planar pursuit-evasion with variable speeds, part 1, extremal trajectory maps

  • U. R. Prasad
  • N. Rajan
  • N. J. Rao
Contributed Papers

DOI: 10.1007/BF00935252

Cite this article as:
Prasad, U.R., Rajan, N. & Rao, N.J. J Optim Theory Appl (1981) 33: 401. doi:10.1007/BF00935252


Pursuit evasion in a plane is formulated with both players allowed to vary their speeds between fixed limits. A suitable choice of real-space coordinates confers open-loop optimality on the game. The solution in the small is described in terms of the individual players' extremal trajectory maps (ETM). Each map is independent of role, adversary, and capture radius. An ETM depicts the actual real-space trajectories. A template method of generating constant control arcs is described. Examples of ETM for an aircraft flying at a constant altitude with fixed and varying speeds are presented.

Key Words

Pursuit-evasiongame barriersdifferential gamesaerial combat

Copyright information

© Plenum Publishing Corporation 1981

Authors and Affiliations

  • U. R. Prasad
    • 1
  • N. Rajan
    • 3
  • N. J. Rao
    • 4
  1. 1.Department of Aeronautical EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.School of Electronic System DesignCranfield Institute of TechnologyCranfieldUnited Kingdom
  3. 3.ISRO Satellite CentreBangaloreIndia
  4. 4.School of AutomationIndian Institute of ScienceBangaloreIndia