## 1 Introduction  
In recent years, with the rapid development of communication and computing technology, people pay more and more attention to the control of multi-agent systems [1; 2; 3]. \"Agent\" can be broadly defined as a computing entity that is adaptive, autonomous, and has a certain life cycle in a particular environment. Drones, driverless cars, robots, etc., can all be called \"Agent\". Apart from these, single-agent has played an important role in aerospace, military, and real life. Furthermore, the development of intelligent control, modern communication technologies, artificial intelligence concepts, etc., as well as people inspired by the phenomenon of animal cluster activity in nature, have pushed agent control research into a new stage of development. By working together, multi-agent can accomplish some parallel, complex tasks, more efficiently than single-agent. For instance, multiple satellites orbiting the Earth to complete designated tasks and multiple drones can work together to transport goods in disaster relief. In recent years, many researchers have considered applying iterative learning control (ILC) to multi-agent systems with repetitive work. ILC is a tracking control method for systems that require high precision and repeat the same actions. In a study by [PERSON] and [PERSON] [4], ILC was applied to the formation control of a multi-agent system for the first time. Since then, more and more researchers have applied ILC to the practical application of multi-agent system. [PERSON], [PERSON], and [PERSON] [5] proposed an ILC law to maintain the flight path of satellite formation. Since the satellite rotates the earth periodically, the position related interference can be considered as the time periodic interference. According to [PERSON] and [PERSON] [6], multiple robots can guarantee formation using iterative learning. Furthermore, in order to ensure the safe running interval of trains, [PERSON], [PERSON], and [PERSON] [7] studied the corresponding ILC scheme of multi train cooperation. In studies by [PERSON] and [PERSON] [8] and [PERSON] and colleagues [9], a group of four rotor aircrafts kept a given formation and accurately tracked the desired trajectory with ILC. However, considering the limited capacity of the communication channel, the actual control design based on wireless communication is difficult. In addition, various industrial production processes and equipment are very complex. For these reasons, communication delay, packet loss, quantization and so on will cause the ILC of multi-agent to not converge [10; 11]. There are specific researches (see [12; 13; 14; 15; 16; 17]) on communication delay and quantization, but few on communication packet loss. [PERSON] and [PERSON] [18] designed an asynchronous event triggering protocol to solve the consistency problem of multi-agent system in the case of external interference, parameter uncertainty, time-delay, and packet loss by \(\Sigma\Delta\) quantizer. By using the extended Lyapunov-Krasovskii functional, a consistency criterion in the form of matrix inequality was derived to ensure the consistency of multi-agent system with delay and packet loss under H1 controller. Firstly, [PERSON] and [PERSON] [19] considered the packet loss problem in the quantitative ILC of a multi-agent system. Considering the nonlinearity of quantization and the randomness of packet loss, a method of reducing learning gain to obtain accurate tracking was proposed. However, the results showed that the convergence rate slows down with the increase of the packet loss rate. All the results from their study [19] are for homogeneous multi-agent systems and assume that multiple agents have the same packet loss rate. The packet loss compensation for heterogeneous multi-agent systems with different packet loss rates is a more challenging problem. This paper explores the ILC method with packet loss compensation for a heterogeneous multi-agent system.