Abstract:
A two-player differential game with an unfixed endpoint is considered. A special feature of the game is the presence of not only a target set but also a lifeline. If the second player steers the lifeline, then the payoff equals infinity. The payoff functional depends on the trajectory of the players and their controls. Special cases of the differential game under consideration are the pursuit–evasion game and time-optimal game. Universal positional strategies are constructed for the game under consideration under the assumption that the Dirichlet problem for the Hamilton–Jacobi equation, related to the differential game, admits a viscosity proximal solution. The construction of universal strategies is based on the concept of a proximal gradient and utilizes the Krasovsky–Subbotin approach. The universality of positional strategies means that for any initial point from a compact set, the feedback strategy is equally effective. In addition, theorems on the evaluation of the guaranteed result of the players are proved.
Fulltext:
PDF file (256 kB)