Mini-Max Incentive Strategy for LQ Stackelberg Differential Games with Uncertainties

Abstract

AbstractThis paper studies the problem of designing an Incentive Strategy for a Two Players Stackelberg Differential Game affected by some sort of uncertainties. As is traditionally understood in the standard theory of incentives, the leader has a complete knowledge of the system parameters of the game as well as the performance objective of the follower, so that he can compute the strategy that will lead the game to the global optimum which is favorable for the leader. Most of the existing work is devoted to this situation, nevertheless the assumption of a complete knowledge even of the game parameters is unrealistic. This paper proposes an Incentive scheme for Stackelberg Games in which the parameters describing the dynamic of the game depends on an unknown vector which belongs to a finite parametric set and the solution of the incentive strategy is given in terms of the worst case scenario. Based on the Robust Maximum Principle the new Incentive scheme is presented in the form of a Mini-Max feedback control. A numerical example illustrates the efectiveness of the approach.