Search

This paper studies the sliding-mode surface (SMS)-based approximate optimal control issue for a class of nonlinear multiplayer Stackelberg-Nash games (MSNGs). First, considering different roles of the players in MSNGs, a hierarchical decision-making process is expressed as designing different cost functions for the leader and the followers. Therein, the leader makes its decision preferentially with consideration of all followers, while each follower responds optimally to leader's strategy simultaneously via Nash games. Then, based on the sliding mode control technology, a novel robust control policy is proposed to solve the coupling Hamilton–Jacobi equations of nonlinear MSNGs. Subsequently, SMS-based critic network is utilized to approximate optimal control inputs for all players. Based on the Lyapunov stability theory, it is strictly proven that all signals of the closed-loop nonlinear systems are uniformly ultimately bounded. Finally, the effectiveness of the proposed method is demonstrated via a simulation example. • The Stackelberg-Nash game (SNG) has one leader and multiple followers. • The SMC method is combined with optimal control design for SNG. • The robust control scheme applies only a critic network. [ABSTRACT FROM AUTHOR]