Stabilization Control of Stackelberg Game-Based System: Continuous-Time Case

This article studies the stabilization control of the Stackelberg game-based system (SGBS) which involves a leader and a follower under continuous time. There are two main contributions: first, the explicit Stackelberg strategy and the optimal performance index under finite horizon are derived based on Riccati equations (REs). Second, the equivalent condition for the SGBS to be stabilizable is obtained, meanwhile, the corresponding Stackelberg strategy and optimal index under this condition are given by REs. Different from the previous works, in the optimization process of the leader, we obtain the linear Stackelberg strategy based on state feedback by applying the matrix maximum principle. Our key technique is solving forward-backward differential equations obtained from the maximum principle.