## 1 Introduction  
In recent years, formation tracking control of underactuated surface vessels (USVs) has attracted considerable interest, as USVs can be widely used in ocean engineering fields [1; 2; 3]. Compared with single vessels, formations offer many advantages. In the course of ocean exploration, the efficiency of a single vessel is low, whereas formations can perform the complex tasks such as pursuit tasks that usually cannot be accomplished by a single vessel. There are various formation control schemes, including the leader-follower approach [4; 5], virtual structure [6], the graph-based mechanism [7], the data-driven model [8], UAV-USV heterogeneous multiagent systems [9] and adaptive fuzzy formation control [10]. In particular, the leader-follower strategy is preferred in ocean engineering applications. The follower maintains a desired distance and angle relative to the leader, and a reference trajectory can be defined by the leader. Therefore, the group behavior is directed by the leader, and the formation stability can be induced by the control law of a single vessel. There are two main challenges that are still worth mentioning. The first challenge is actuator saturation, which can severely degrade the closed-loop system performance [11]. In practice, each actuator of a vessel can only provide a limited force or torque. To reduce the risk of actuator saturation and enhance system performance, some methods have been proposed in recent years. To avoid poor tracking performance in formation control, generalized saturation functions combined with formation tracking errors were employed to handle the input saturation problem [12]. To solve the problems of input saturation and underactuation simultaneously, additional variables were induced to velocity errors in the body-fixed frame [13; 14]. Non-linear saturation of an actuator was approximated by a Gaussian error function [15] such that an anti-saturation controller could be designed. An auxiliary dynamic system was constructed to solve the input saturation problem [16], with the auxiliary dynamic system designed as a second-order system, providing a conservative input signal. A first-order auxiliary system was designed in [17] and employed to deal with input saturation of the rudder. The authors of [18] used an auxiliary system to solve the problem of input saturation, which was combined with a collision-avoidance control strategy to provide tracking control for dynamic vessel positioning. However, the limited acting frequency actuators was not considered in the articles mentioned above. High-frequency action may lead not only to mechanical abrasion but also to a short service life [19]. Input saturation and actuator rate limits were considered in [20], and a non-linear controller was designed based on dynamic surface control and backstepping technology. Additional controllers were proposed to deal with actuator magnitude and rate saturation in [21]. The authors of [22] considered actuator saturation with limited magnitude and rate and designed a sliding model controller. In [20; 21; 22], Zeno behavior was avoided because the acting frequency of actuator was bounded. A controller combined with an event-triggered condition was proposed in [23], and the triggered condition was designed based on the flow time and error function; however, this configuration still resulted in long action times of the actuator. An event-triggered distributed controller was employed in [24], and the triggered condition was designed based on changes in amplitude of input signals. The authors of [25] proposed an event-triggered control law, and an event-triggered mechanism was used to reduce the execution frequency of actuators. The event-triggered mechanism was designed in the controller-to-actuator channel, and the execution rate of the actuator was reduced. The second significant challenge is the uncertainties. Because of the working condition of the surface vessel, uncertainties include model uncertainties and environmental disturbances.