Multi-Player Robust Control of Stackelberg Games via Adaptive Dynamic Programming

Abstract

In this paper, the hierarchical optimization problem of multi-player systems with matched uncertainties is investigated via adaptive dynamic programming. In the hierarchical optimization problem, there exist one leader and multiple followers, the leader chooses a policy in advance based on the actions of the followers, and the followers make optimal responses to the leader's policy. The optimal policies of the leader and the followers form the Stackelberg equilibrium. By designing appropriate value functions for the leader and the followers, the hierarchical optimization problem is formulated as a Stackelberg game and the robust stabilization problem is transformed into an optimal regulation problem. Moreover, the critic-only structure is established to obtain the approximate Stackelberg equilibrium. Theoretical analysis shows that the developed ADP-based robust control guarantees the closed-loop system to be asymptotically stable. Finally, simulation example is adopted to verify the effectiveness of the present scheme.