## 1 Introduction
The tracking HJI equation is solved by off-policy reinforcement learning. In [20; 21], Adaptive critic designs (ACD) are used to solve the zero-sum problem that external disturbances have an impact on system performance. However, in engineering applications, the controller requires high physical characteristics and security, which is usually limited by the threshold. In addition, the design and analyzable methods of the control system also have higher requirements. It is not only necessary to achieve the control design goal to ensure the stability of the dynamic system but also to consider the control performance of the system to save energy and reduce consumption. The above iterative methods mostly use the time-triggered mechanism of periodic sampling to solve the nonlinear zero-sum game problem with actuator saturation. To reduce unnecessary data transmission and frequency update between components, the event-triggered mechanism is introduced into adaptive dynamic programming for the first time in [22]. A controller with sampling states limited by a triggering condition is designed, which not only ensures the stability and optimality of the system, but also reduces the controller update. For the system with constrained input, [23; 24] propose an approximately optimal control structure based on the event-triggered strategy, which makes control laws update non-periodically to reduce computation and transmission costs, and ensures the uniform ultimate boundedness of the event-triggered system. The designed triggering condition is the key to the event-based controller. Not only does the triggering condition have a non-negative triggering threshold but it avoids Zeno behavior. In [25], an event-driven controller is designed, and the triggering condition should not only have a non-negative triggering threshold but also the Zeno behavior is free. In [26], the IRL-based event-triggered algorithm is used to solve the partially unknown nonlinear system. The critic-network updates periodically and the actor-network updates non-periodically to approximately acquire the performance index function and control law. The good convergence of the NN weight is theoretically proved and effectively avoids the Zeno phenomenon. For the system with unknown disturbance, the robust controller is designed by using the \(H_{\infty}\) control method. In [15], an event-triggered \(H_{\infty}\) controller is structured, which introduces the disturbance attenuation level into the triggering condition, and ensures that the triggering threshold is non-negative by selecting appropriate parameters. The control law is updated with an event-triggered strategy, and the perturbation law is adjusted under the time-triggered mechanism. At present, the event-triggered ADP algorithm has been applied to optimal regulation problem [27; 28], optimal tracking control [29], zero-sum game [30; 31; 32], non-zero-sum game [33; 34], robust control problem [35; 36]. However, most studies are based on identification-critic NNs or critic-actor-perturbation NNs structure to approximate obtain the solution of the HJI equation for the zero-sum game problem, which often increases the communication load such as actuators and controllers, and increases the loss of resources and costs [37; 38]. Therefore, an event-triggered ADP method is proposed to solve the \(H_{\infty}\) optimal control problem for partially unknown continuous-time nonlinear systems with constrained input, and the structure of a single-critic network is constructed to acquire approximately the solution of the HJI equation. This paper aims to achieve the following aspects:  
1. Based on the event-triggered control, the triggering condition with the level of disturbance attenuation is developed to limit the sampling states of the system, and the appropriate level of disturbance attenuation is selected to ensure that the triggering condition remains non-negative. 2. An event-triggered \(H_{\infty}\) input-constrained nonlinear system controller is designed.