Necessary conditions for robust Stackelberg equilibrium in a multi‐model differential game

SUMMARY This paper presents the formulation of a new concept dealing with a robust Stackelberg equilibrium for a multiscenario or multiple models two‐player differential game. The game's 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 is how to design a mini‐max strategy for each player which guarantee an equilibrium for the worst case scenario. Based on the robust maximum principle, the general necessary conditions for a game to be in robust Stackelberg equilibrium are presented. A numerical procedure for resolving the case of linear affine‐quadratic game is designed.Copyright © 2011 John Wiley & Sons, Ltd.