Galerkin-based method for a differential game of two-dimensional distributions

This paper presents a differential game of two hostile teams in a two-dimensional operational field. The authors consider numerous players who spread as if they formed a continuous distribution in the field. The mathematical model of the motion of such players can be described by partial differential equations, which resemble traffic equations. The state of the system thus consists of the geographical distributions of the numbers of players for different teams over the field, namely the densities of the players. In this paper, the authors derive a Galerkin-based finite-dimensional feedback controller for the differential game. The controller gains are obtained by using the sequential linear-quadratic algorithm.