The geometric approach to the construction of the barrier surface in differential games
The paper deals with qualitative pursuit-evasion differential games. The known Issac's geometric method for the construction of the barrier surface is examined and developed. The authors present a new geometric second-order necessary condition that a valid barrier surface must satisfy. The named geometric approach allows the authors to investigate the parameter dependence in the special cases of the Homicidal Chauffeur differential game and the Game of two cars and in particular, to explain the ``non-classical'' situations in these games. Some other new results concerning the barrier surfaces for the above two games are also presented in the paper.
qualitative pursuit-evasion differential games
geometric second-order necessary condition
scientific article; zbMATH DE number 4029315