Robust Stackelberg Equilibrium for a Multi-Scenario Two Players Linear Affine-Quadratic Differential Game

This paper presents the formulation of a new concept dealing with a Robust Stackelberg equilibrium for a multi scenario or mutiple models of a linear affine-quadratic game. The game dynamic is given by a family of N different possible differential equations (MultiModel representation) with no information about the trajectory which is realized. The robust Stackelberg strategy for each player must confront with all possible models simultaneously. The problem consists in the designing of min-max strategies for each player which guarantee an equilibrium for the worst case scenario. Based on the Robust Maximum Principle, the general conditions for a game to be in Robust Stackelberg Equilibrium are also presented. A numerical procedure for resolving the case of LQ differential game is designed.