Guaranteed Strategies for Nonlinear Multi-Player Pursuit-Evasion Games

In this paper, we provide a methodology to design strategies for either guaranteed capture or guaranteed evasion in the case of pursuit-evasion games with multiple players which are represented by nonlinear dynamic models. This methodology is based on the continuously differentiable upper and lower approximations of the minimum and maximum function of an arbitrary number of arguments, comparison principle, and differential inequalities.