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Proportional navigation and the game of two cars

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Abstract

A stochastic version of Isaacs's game of two cars is considered. The motion of the players is confined to the pursuer's effective operation zoneD P, and the cost function of the game is the probability of the event: {Before the evader enters his safe zone, the evader enters the pursuer's killing zoneK P, at somet, 0≤t≤T, or the evader stays at the domainD P−K P, for allt∈[0,t 0],t 0>T}. By numerically solving a nonlinear parabolic boundary-value problem on a generalized torus in ∝3, it is shown that, for a range of values of some parameter, a proportional navigation guidance law is an optimal feedback pursuit strategy.

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Authors and Affiliations

  1. Center for Advanced Computing and Decision Support, CSIR, Pretoria, South Africa

    Y. Yavin (Chief Specialist Researcher) & R. de. Villiers (Senior Scientist)

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  1. Y. Yavin
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  2. R. de. Villiers
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Communicated by J. V. Breakwell

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Yavin, Y., de. Villiers, R. Proportional navigation and the game of two cars. J Optim Theory Appl 62, 351–369 (1989). https://doi.org/10.1007/BF00939811

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  • DOI: https://doi.org/10.1007/BF00939811

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