## 1 Introduction  
The control problems of multi-agent systems have been widely studied in the past two decades, such as distributed control problems [1, 2], robust control problems [3, 4], formation control problems [5, 6], and so on. Additionally, many researchers have paid attention to the control problems of practical multi-agent systems because they have obvious advantages in solving complex control problems. In [7], the authors implemented the task allocation problem for wireless sensor networks using the multi-agent method. To achieve the finite-time tracking control problem of robotic systems, the authors of [8] proposed an improved integral sliding mode control method. In addition, the event-triggered adaptive tracking control problems of six-degrees-of-freedom unmanned aerial vehicles were solved in [9, 10]. However, it should be pointed out that multi-agent systems may not be accurately modeled due to the existence of uncertain nonlinear dynamics, unknown disturbances, or parameter uncertainties. Therefore, how to solve the control problems of nonlinear multi-agent systems caused by these factors is worth studying. Many excellent recent achievements for control problems of nonlinear multi-agent systems can be found in the existing literature. In [11], a class of uncertain lower triangular, nonlinear, multi-agent systems was addressed, where an adaptive asynchronous event-triggered strategy was designed to achieve the distributed consensus tracking problem. In [12], an exosystem observer-based output regulation controller was presented to solve the distributed optimization problem of uncertain heterogeneous linear multi-agent systems. Moreover, a distributed tracking controller for a class of uncertain heterogeneous nonlinear multi-agent systems was investigated in [13]. In addition, for the tracking control problems of uncertain fractional-order multi-agent systems [14; 15], uncertain multi-agent systems with stochastic measurement noises [16], and stochastic multi-agent systems with uncertain actuator faults [17], some scholars have carried out research and put forward their own control methods. Although these papers studied the control problems of multi-agent systems, there is no in-depth study on the finite-time control problem of multi-agent systems. In addition, some control methods are often used, such as the model predictive control method [18], metaheuristic optimization algorithm [19; 20], and sliding mode control method [21], to solve the control problems of complex nonlinear systems. Nevertheless, as an effective tool, the backstepping control technique is widely applied for uncertain nonlinear systems [22; 23; 24]. It should be noted that repeated differentiation of the virtual control law is required when applying the backstepping control method. This may cause the \"explosion of complexity\" issue. For this reason, the dynamic surface control technique is proposed to improve the traditional backstepping control method, and many meaningful results can be found in [25; 26; 27]. For multi-agent systems, some control schemes are addressed, such as the adaptive cooperative neural dynamic surface control scheme [28], the robust adaptive distributed dynamic surface control scheme [29], and the event-trigger-based recursive sliding mode dynamic surface scheme [30], to solve the desired control problems. Therefore, the dynamic surface control method provides a good solution for the control problems of complex uncertain nonlinear multi-agent systems. For practical systems, sometimes we need to consider the issue of control direction, which is the sign of the control coefficient. In many existing results, the sign is considered to be known and usually to be assumed positive. However, the control direction may not be predicted in advance due to the existence of unpredictable states or uncertainties. As a common processing method, the Nussbaum gain function control technique is widely used to solve the problems of unknown control directions [26; 31; 32; 33; 34].