Robust ADP-based control for uncertain nonlinear Stackelberg games

Stackelberg games allow players to access system information differently and take actions asynchronously. This paper introduces a robust adaptive dynamic programming-based method to solve the nonlinear two-player Stackelberg game subject to external disturbances. Combined with a neural network identifier, our method is implemented on the actor-critic-disturbance structure to approximate the optimal value function, i.e., the corresponding Stackelberg equilibrium. With the aid of costate, we transform this leader-follower optimization problem into solving two parametric equations and a costate equation. The coefficients of critic approximators and the costate are updated simultaneously to reach the Stackelberg equilibrium. The proposed control method finds real-time approximations of the Stackelberg-Saddle equilibrium while ensuring the closed-loop system's stability. Finally, the simulation example shows the effectiveness and advantage of our method.