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This paper investigates the issue of event-triggered optimal control for saturated nonlinear systems with full state constraints. A smooth function is defined to map the constrained states, then the considered system can be transformed into a state unconstrained system with unknown approximate errors. In addition, a novel event-triggered mechanism is proposed via an adaptive dynamic programming algorithm, which can obtain the optimal control law without constructing the so-called event-triggered HJB equation. Moreover, in order to conquer the difficulty caused by the persistence of excitation conditions, the experience replay technique is utilized to design the critic update law. Meanwhile, it is demonstrated that all signals are uniformly ultimately bounded. Finally, two simulation examples are given to demonstrate the effectiveness of the control strategy. [ABSTRACT FROM AUTHOR]

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]