Games of Simple Pursuit and Approach on Two-Dimensional Cone

Arik Melikyan
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Arik Melikyan: Institute for Problems in Mechanics, Russian Academy of Science

Chapter 5 in Generalized Characteristics of First Order PDEs, 1998, pp 169-198 from Springer

Abstract: Abstract In this chapter local necessary conditions of the previous chapter are used to construct the complete (global) solutions. Two differential games, that of pursuit and of approach, are considered, in which players are velocity controlled points of three-dimensional Euclidean space, performing simple motion on the surface of a two-dimensional cone, i.e. at each moment of time they can choose arbitrary directions of their velocities which are tangent to the surface of the cone and restricted in values. In case the pursuer has advantage in speed, the game of pursuit with the capture time as the cost function is considered; in opposite case (faster evader), the game of approach is considered, the cost function being the minimal distance between players during infinite time-interval of motion.

Keywords: Critical Curve; Feedback Strategy; Singular Surface; Geodesic Line; Primary Domain (search for similar items in EconPapers)
Date: 1998
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DOI: 10.1007/978-1-4612-1758-9_6

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