Journal of Optimization Theory and Applications

, Volume 56, Issue 2, pp 179–204 | Cite as

An optimal evasion problem: Complete global solution

  • M. Pachter
  • E. Kreindler
Contributed Papers


We consider a collision avoidance optimal control problem. The kinematics is modelled by a maneuverable pointE in the plane, with a limited rate of turn (a car à la Isaacs), that is moving at a constant speedvE and is trying to avoid a circular disc of radiusl centered around a pointP, known to move at a constant speedvP in the positive direction of they-axis.

Global questions, answered analytically in the paper, are these: (i) the initial positions are determined ofE, relative toP, for which the capture ofE byP is assured—we characterize the capture zone in the state space; (ii) given thatE is initially in the capture zone, we solve the optimal control problem of steeringE to maximize the bearing ofE fromP at the instant of capture; (iii) we investigate the dependence of the answers to (i) and (ii) on the problem parameters α≜vP/vE>1 andl.

We solve completely a relatively simple, but practically meaningful, optimal evasion problem, not, to our knowledge, previously published.

Key Words

Collision avoidance optimal evasion differential games 


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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • M. Pachter
    • 1
  • E. Kreindler
    • 1
    • 2
  1. 1.National Research Institute for Mathematical SciencesCSIRPretoriaSouth Africa
  2. 2.Department of Electrical Engineering, TechnionHaifaIsrael

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