  This paper is about a set-based computing method for solving a general class
of two-player zero-sum Stackelberg differential games. We assume that the game
is modeled by a set of coupled nonlinear differential equations, which can be
influenced by the control inputs of the players. Here, each of the players has
to satisfy their respective state and control constraints or loses the game.
The main contribution is a backward-forward reachable set splitting scheme,
which can be used to derive numerically tractable conservative approximations
of such two player games. In detail, we introduce a novel class of differential
inequalities that can be used to find convex outer approximations of these
backward and forward reachable sets. This approach is worked out in detail for
ellipsoidal set parameterizations. Our numerical examples illustrate not only
the effectiveness of the approach, but also the subtle differences between
standard robust optimal control problems and more general constrained
two-player zero-sum Stackelberg differential games.
