## 1 Introduction
The event-triggered signal based on a relative threshold is introduced to reduce the communication burden, and the dynamic surface control technology is used to solve the problem of computational complexity. In response to the need to reduce the frequency of event triggering, reference [19] introduced a dynamic event-triggering mechanism that optimizes the utilization of communication resources via internal dynamic variables. This mechanism can adaptively adjust event-triggering conditions based on changes in the system state, thus more effectively achieving consistency control objectives [20]. This further proves that the dynamic event-triggering method can significantly reduce communication overhead and improve system stability and performance. Referring to [21], it was determined how backstepping controllers affect parameter uncertainty and how they are used to manage the fixed-time creation of a heterogeneous multi-agent system. Reference [22] applies the integral to create a sliding mode using a sliding mode control mechanism controller, considering the effects of external interference. Multi-agent systems typically have constrained communication resources in real-world applications. Discontinuous control techniques can conserve energy and cut back on communication. Reference [23] investigated the fuzzy distributed impulsive control in the nonlinear multi-agent system protocol and achieved system consistency with regard to denial-of-service (DoS) assaults. Multi-agent systems, including [24; 25], have extensively exploited event-triggered control techniques. Reference [24] studied the distributed two-part tracking control protocol based on event triggering for a stochastic multi-agent nonlinear system with input saturation. By constructing a novel observer and adopting an event-triggering mechanism, boundedness and distributed consistency tracking of signals were achieved. For linear multi-agent systems, reference [25] put forth a fully distributed event-triggered control approach. In addition, control protocols can also be used to achieve self-triggering. Reference [26] studied the robust synchronization problem of a class of master-slave neural networks with network-induced delays, unknown time-varying uncertainties, and exogenous disturbances, and developed an event-triggered control protocol to obtain the synchronization of MSNNs. While the aforementioned literature references do consider event triggering to reduce communication, they do not specify the timing. In order to correct the issue where the convergence time of multi-agent systems depends on initial conditions, it is crucial to conduct research on the timing control issues associated with multi-agent systems. The event-triggered controller utilizing sliding mode control technology was suggested in reference [27] in order to achieve the timing consensus of the leader polling multi-agent system. A high-order leader-follower multi-agent system's fixed-time technique was examined in reference [28] to assess the leadership state and arrive at a tracking consensus simultaneously, and reference [29] further discussed how to implement the fixed-time strategy in the face of unknown interference. In reference [30], the weighted directed topology-based fixed-time consistent tracking control issue of second-order multi-agent systems with bounded input uncertainty was examined. Fast and stable consistency tracking control has been achieved by forming unique non-singular fast terminal sliding with fixed-time surfaces and distributed control protocols. Reference [31] investigated how a multi-agent system's fixed-time group consistency was affected by external interference and constructed two fixed-time guidance control algorithms for the system. References [32; 33] discussed the fixed-time consistency of two different forms of multi-agent systems. Regarding a first-order heterogeneous multi-agent system that is nonlinear to achieve timing consistency, reference [32] provided a new protocol design framework.