## 1 Introduction
It can be clearly detailed that the system inputs remain unchanged between two consecutive triggering times, which are determined by the aforementioned events, i.e., the events may be considered as a threshold and constructed by tracking errors. A key issue fascinating the scientific community to date is how to propose a triggering rule that moderately reduces the number of triggering times while maintaining satisfactory control performance and excluding the Zeno behavior, which means infinite numbers of triggering times in a finite time interval [18]. The authors in [19] proposed an aperiodic sampled-data formation protocol for MAS, in which each agent solely exchanges its information with its neighbors at a specific discrete time. In the continuous control system design, instead of using the static event-triggered rule, a dynamic event-triggered control that has evident merits in lessening the risk of network congestion has been considered attractive in many recent studies (see [20; 21; 22; 23] and the references therein). In [24], a dynamic event triggering mechanism was proven to have a minimum triggering time that was greater than that of the static counterpart, leading to a reduction in redundant workloads and network congestion. Based on the dynamic triggering rule for the distributed formation control, the authors in [25] proposed an event-triggered communication mechanism to achieve a fixed formation of multiple ground robots. The study [26] presented a dynamic and a self event-triggered control for one-integrator MASs to achieve an average consensus, where the Zeno behavior was excluded. By considering an agent as a leader, second-order MASs that used event-sampling schemes achieved a consensus problem based on a leader-follower protocol in [27]. These existing results somehow can be enriched by expanding with the time-varying formation control of multi-agent systems. Motivated by the above observations, this paper proposes a dynamic event-triggered control algorithm for the time-varying formation of multi-agent systems. The dedicated algorithm guarantees that the group of agents is capable of tracking the desired time-varying formation, as well as significantly reducing the number of trigger times in each agent in comparison with that of the conventional continuous control algorithm. In our approach, the control synthesis is based on a new control Lyapunov function such that each agent possesses a distributed controller and an event triggering mechanism, leading to the exponential asymptotic convergence of the formation tracking errors. Additionally, the new triggering mechanism is designed to exclude the Zeno behavior. To summarize, our main contributions can be highlighted as follows:  
1. A distributed dynamic event-triggered time-varying formation control algorithm is proposed for a group of agents, in which each agent includes position and attitude dynamics. To the best of our knowledge, comparatively little progress has been made towards time-varying formation control with a dynamic event triggering mechanism. 2. In the control design for the systems, one of the most challenging problems is that the distributed property is a compulsory requirement in both controllers and event triggering mechanisms. Based on a new control Lyapunov function, a state feedback controller and a dynamic event triggering mechanism are proposed. As a result, the proposed control law guarantees that the group of agents asymptotically tracks the desired formation trajectory. Finally, the performance of the proposed controller is illustrated via an example of quadcopter formation control. 3. Another challenging problem arises from the time-varying formation control. It is worth noting that the control inputs depend not only on the states of the agent, but also the desired formation trajectory, which makes our approach different from the existing approaches reported in [16; 17; 24; 25; 26].