switching directed network topologies is considered in [8]. In [9], a type of feedback control law with velocity measurements is proposed for double-integrator MASs and an experimental platform consisting of five wheeled mobile robots is used to validate the result. To reduce the communication burden, [10] developed a finite-time containment control algorithm for double-integrator MASs using only position measurements. In [11], the effects of time-varying delays are taken into consideration, where the linear matrix inequality method and the Lyapunov functional method are jointly used to ensure the containment. In [12], the noise in agent information transmission is formulated and corresponding time-varying state feedback containment control laws are proposed for both first-order and second-order integral MASs. As a extension of [12], ref. [6] considers both measurement noise and polynomial disturbance in high-order integral MASs, where a containment controller is designed with a proportional term and the nth-order integral terms. Recent work begins to focus on the general linear or nonlinear MASs. In [13], based on the relative outputs of neighboring agents, dynamic observer-type containment controllers are built for both continuous-time and discrete-time general linear MASs. The results of time-varying uncertainties and constant time delays for general linear MASs are shown in [14; 15], respectively. As a special kind of nonlinear agents, the rigid body MASs formed by Euler-Lagrange expression is studied in [16], in which a sliding-mode estimator based containment controller is given. Considering the parametric uncertainties of Euler-Lagrange MASs, [17] develops a modified sliding mode containment controller based on the one in [16] without using velocity information. Some results of more general nonlinear agents have also been reported. In [18], the fuzzy logic is utilized to approximate the dynamics of Lipschitz nonlinear MASs and an observer-based containment controller is designed. In [19], sliding mode controllers are proposed to address the finite-time containment problem of MASs with Lipschitz-like nonlinearity and external disturbances. Based on neural networks (NNs) and backstepping techniques, a finite-time containment controller is applied to the high-order nonlinear MASs with dynamic uncertainties in [20]. Although massive achievements has been obtained in [6; 7; 8; 9; 10; 11; 12; 13; 14; 15], some limitations still exist for the current algorithms. The containment control schemes used in [6; 7; 8; 9; 10; 11; 12; 13; 14; 15] are designed for known linear agents. However, in coordination tasks, the practical MASs always suffer from the effects of unmodelled dynamics and nonlinearities. Thus, the control laws in [6; 7; 8; 9; 10; 11; 12; 13; 14; 15] may face performance deterioration in real implementation. The methods presented in [6; 7; 8; 9; 10; 11; 12; 13; 14; 15] require that the controlled MASs should be the affine nonlinear system, i.e., the control input term is assumed to be known and linear. Furthermore, the NNs based controller needs extra training processes [20], and the selection of fuzzy membership functions in [18] heavily depends on the experience of users. Therefore, the containment control design for unknown nonlinear MASs is still an open and challenging problem. Model-free adaptive control (MFAC), initially proposed in [21], is an effective approach to deal with unknown nonlinear systems. With 20 years of development, MFAC has now provided a systematic control framework with a wide range of engineering applications [22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33]. The partial-form dynamic linearization based MFAC controller is designed for a class of single-input and single-output unknown nonlinear system in [22], and it is extended to the multi-input and multi-output system in [23]. Based on the view of an ideal controller, the controller dynamic linearization based MFAC is proposed in [24] and then enhanced by radial basis function NNs in [25].