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.

本文研究了为受某种不确定性影响的领导者-追随者动态博弈设计激励策略的问题。正如传统激励标准理论所理解的那样，领导者完全了解游戏参数，包括追随者的绩效指标。这样他就可以计算出使游戏达到对他有利的全局最优的策略。目前的大部分工作都是针对这种情况的。然而，这样的假设是不现实的。本文提出了一种激励方案，其中游戏的动态取决于属于有限集的未知值。激励策略的解决方案是根据团队最佳解决方案的最坏情况来计算的。基于鲁棒最大原则，新的激励以最小最大反馈控制的形式呈现。两个数值例子说明了该方法的有效性。