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This paper studies the problem of designing an incentive strategy for a leader–follower dynamic game affected by some sort of uncertainties. As is traditionally understood in the standard theory of incentives, the leader has complete knowledge of the game parameters, including the follower's performance index. So then he can compute the strategy that will lead the game to the global optimum that is favourable for him. Most of the current work is devoted to this situation. Nevertheless, such an assumption is unrealistic. This paper proposes an incentive scheme in which the game's dynamic depends on an unknown value that belongs to a finite set. The solution of the incentive strategy is computed in terms of the worst-case scenario, of the team's optimal solution. Based on the Robust Maximum Principle, the new incentive is presented in the form of a mini-max feedback control. Two numerical examples illustrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]