An optimal evasion problem: Complete global solution
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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 WordsCollision avoidance optimal evasion differential games
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