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We study pursuit-evasion differential games between a faster pursuer movingin 3D space and an evader moving in a plane. We first extend the well-knownApollonius circle to 3D space, by which we construct the isochron for theconsidered two players. Then both cases with and without a static target areconsidered and the corresponding optimal strategies are derived using theconcept of isochron. In order to guarantee the optimality of the proposedstrategies, the value functions are given and are further proved to be thesolution of Hamilton-Jacobi-Isaacs equation. Simulations with comparisonbetween the proposed strategies and other classical strategies are carried outand the results show the optimality of the proposed strategies.

Pursuit-evasion differential games of players with different speeds in spaces of different dimensions