To address the repetitive tasks over a finite time interval, model-free adaptive iterative learning control (MFAILC) is presented in [26]. It is reported in [27] that MFAC has been applied to over 150 yields. The latest applications and advances can be found in [28; 29; 30; 31; 32], including weld penetration [28], steam-water heat exchanger [29], traffic systems [30; 31], and the stability analysis of full-form dynamic linearization based MFAC [32]. For the brief review of MFAC, readers are referred to [27; 33]. MFAC has also been employed in the coordination of MASs [34; 35; 36; 37; 38; 39; 40; 41; 42]. MFAC is first used to address the consensus problem for a group of unknown heterogenous nonlinear MASs in [34]. Based on the controller dynamic linearization technique and Newton-typeoptimization method, a data-driven ideal leader-follower consensus tracking algorithm is designed in [35]. Then, the consensus tracking issue under repetitive environment is solved by using MFAILC in [36]. In [37], a MFAC based predictive consensus scheme is presented for MASs with communication constraints. In [38], the consensus problem for the MASs under time delays is solved by the Smith estimator enhanced MFAC scheme. For the formation control of MASs, [39] gives a data-driven formation control scheme based on MFAILC. Considering the iterative-varying disturbance, the algorithm in [39] is extended to a robust form formation control law in [40]. In [41], an event-triggered MFAC method is used to perform the containment task where the MASs are suffering from denial-of-service attacks. A model-free adaptive containment control scheme is investigated for a class of multi-input multi-output nonlinear MASs in [42]. However, the MASs in [34; 35; 36; 37; 38; 39; 40] only contain one single leader, while no exploration has been conducted for multileaders case. The work in [41; 42] only found the result that the defined local containment error is bounded or converged, which is not exactly equivalent to the containment goal. Inspired by above observations, a novel distributed model-free adaptive containment control scheme is proposed in this paper. Compared with existing work, the main contributions of this work are threefold:  
1. A novel distributed model-free adaptive containment controller is developed. Compared with previous work [34; 35; 36; 37; 38; 39; 40], the MASs extend to the multiple-leader case. By virtue of the MFAC framework, this controller is endowed with the data-driven feature, i.e., the design process only utilizes I/O data of the agents rather than their mathematical models. Moreover, this method does not need the extra training process that is required in the NNs based algorithm [20]. 2. The global containment error is proposed to overcome the analysis nonequivalent problem in [41; 42]. Then, the Lyapunov function based stability analysis is conducted to guarantee that the containment goal is achieved, which is different from the conventional contraction mapping principle used in MFAC based protocols (e.g., ref. [35]). In addition, the follower dynamics considered in this paper can contain the nonaffine nonlinear property, whereas the follower dynamics appearing in [6; 7; 8; 9; 10; 6; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20] are either affine or linear. 3. The control scheme is further extended to a time-switching topology and dynamic leaders case, which makes the controller more applicable and flexible in real implementation. The remaining part of the paper is organized as follows. Section 2 presents some preliminary knowledge and gives problem formulation. Section 3 shows the main results, including the controller design and stability analysis. Section 4 extends the existing result to a time-switching topology and dynamic leaders case. In Section 5, three numerical examples are provided. Finally, the conclusion is discussed in Section 6.