## 1 Introduction  
Wireless sensor networks and system collaborations with multiple agents [1] can be combined to handle complexity, improve system performance, and use wireless sensor networks in a variety of contexts. This integration not only advances the field of control but also provides more possibilities for practical applications. The collaborative control of multi-agent systems involves interactions and cooperation among multiple agents, requiring the overcoming of challenges such as heterogeneity and uncertainty. The realm of control, such as cluster control [2; 3; 4] and formation control [5; 6; 7], has been a significant issue because it involves the interaction and cooperation between multiple agents, needs to solve complexity, optimize system performance, apply to a wide range of fields, and overcome challenges such as heterogeneity and uncertainty, so as to promote the development and practical application of the control field containment control [8; 9; 10; 11; 12], etc. The goal of containment control is to promote collaboration and cooperation in the multi-agent system, emphasize respect for the objectives of each agent when resolving conflicts and coordinating decisions, and seek to maximize common interests. All states of followers must converge to the leaders' convex hull. The consistency problem under study is also known as containment control when the multi-agent system contains a large number of leaders. A high-frequency feedback was proposed in reference [4]. This involved clustering for a multi-agent system with an unknown parameter in robust control. Reference [5] studied the issues of distributed simultaneous estimation and formation control within the same population of mobile agents with limited communication, perception, and computingcapabilities. A novel scalable algorithm was proposed, achieving convergence of global formation statistics and the decoupling of estimation and control performance. Reference [8] investigated how to control confinement in a second-order linear multi-agent system. We investigated a time-varying triggering threshold event-triggered control technique that takes both uniform and irregular input delays into account. The general linear multi-agent system's creation, containment, and constraint tracking under time-varying control inputs were explored in reference [13]. It proposes a formation containment-tracking protocol that achieves formation, containment, and constraint tracking of intelligent agents by considering the influence of neighboring relative information and unknown inputs from tracking leaders. Reference [14] investigated the nonlinear multi-agent system's finite time constraint control problem, and used fuzzy logic systems to approximate system dynamics. By using nonlinear transformation functions to transform state constraints into unconstrained ones, the follower's convex hull is converged in a finite amount of time using adaptive fuzzy control. In [15], the convergence time of the average consensus problem for networks with heterogeneous random link failures is studied and the influence of event-triggered communication on consensus performance is considered. A large number of simulations are carried out to verify the reliability of the method. In [16], inspired by the cooperative control, a fully distributed and delay-tolerant secondary control scheme is developed for the droop-controlled AC microgrid. The hierarchical control structure of the distributed energy unit is considered to ensure the active power sharing between the three DER units. This article examines numerous control protocols in order to adapt to distinct needs and application histories. Based on the switching topology, reference [17] studied the event-triggered dichotomous consistency of multi-agent systems. In [18], for a class of strict feedback nonlinear systems with external disturbances, a robust fuzzy adaptive prescribed performance finite-time control strategy based on event-triggering is proposed.