# Event-Triggered MFAILC Bipartite Formation Control for Multi-Agent Systems Under DoS Attacks
## 1 Introduction  
The control of a single agent is no longer sufficient to meet the demands of complicated activities due to the recent rapid development of agent applications in a variety of industries. As a result, multi-agent systems (MASs) formation control has attracted significant attention from scholars and researchers. MASs are widely applied to collaboratively accomplish various complex tasks, such as target tracking [1], UAV swarm missions [2], and environmental detection [3]. Formation control is one of the core functions of MASs, with the primary objective of controlling multiple agents to form a specific formation for cooperative operations. Currently, increasing research efforts have been directed toward formation control, leading to numerous achievements. For example, ref. [4] studies formation control for quadrotor UAVs, while ref. [5] discusses formation control for underwater vehicles. It is worth noting that most existing studies adopt model-based control (MBC) methods to address such problems, requiring an accurate mathematical model of the MASs and assuming that all agents have identical structures. However, in practice, obtaining theplant's accurate mathematical models is challenging, and MASs often consist of heterogeneous agents operating in complex environments with numerous uncertainties. Therefore, MBC methods are difficult to generalize and apply to practical systems. To address this challenge, data-driven control (DDC) methods have gained increasing attention, as they avoid the need for accurate data models. Various DDC approaches have emerged, such as reinforcement learning control [6], model-free adaptive control (MFAC) [7; 8; 9], and iterative learning control (ILC) [10; 11; 12]. Among these methods, MFAC designs controllers are solely based on the input/output (I/O) data of the controlled system, without requiring implicit or explicit system models, making it particularly suitable for heterogeneous MASs. The model-free adaptive iterative learning control (MFAILC) method combines MFAC and ILC and is effective for controlling unknown nonlinear non-affine systems with repetitive operations. This method ensures monotonic convergence of system output errors along the iteration axis. Ref. [13] studies a bipartite formation event-triggered control scheme for single-input single-output (SISO) systems, introducing an observer to estimate outputs and designing event-triggered conditions based on the difference between observed and actual outputs. [PERSON]. [14] employs the matrix transformation and the property of the nonnegative matrix, guaranteeing the iterative asymptotic convergence of the error of the SISO-type MASs under the structurally balanced digraph with an oriented spanning tree. Moreover, information exchange between agents relies on network communication. The stability and security of formation systems are now significantly impacted by network attacks due to the rapid growth of network technology. Information transmission channels between agents often experience instability and physical limitations, making MASs susceptible to various network attacks, such as denial-of-service (DoS) attacks, deception attacks, and replay attacks [15; 16; 17]. Among these, DoS attacks are the most common, causing system instability or even loss of control. Therefore, addressing formation control problems under network attacks has become a research hotspot for MASs. Event-triggered mechanisms, which update the controller only when certain triggered conditions are met, can significantly reduce communication burdens and computational pressure [18], thereby alleviating the impact of DoS attacks to some extent. However, they cannot entirely eliminate the adverse effects caused by DoS attacks. Ref. [19] proposes a resilient event-triggered mechanism that effectively mitigates periodic DoS attacks while conserving network resources.