H∞-Constrained Incentive Stackelberg Game for Discrete-Time Systems with Multiple Non-cooperative Followers*

In this paper, an H∞-constrained team-optimal strategy of an incentive Stackelberg game for a class of discrete-time system with an external disturbance is investigated. The team-optimal solution for the leader is achieved in contrast to multiple non-cooperative followers' optimal state feedback gain. The solution sets for incentive Stackelberg strategy are found by solving a set of backward difference Riccati equations (BDREs) in the finite-horizon case. On the other hand, it is shown that the results for the infinite-horizon case are found by solving a set of algebraic Riccati equations (AREs). In particular, it is indicated that the team optimal solutions are yielded even though noncooperative strategy is considered for the multiple followers. In order to demonstrate the effectiveness of the proposed method, a numerical example is given.