This paper deals with the robust consensus tracking problem for a class of heterogeneous second-order nonlinear multi-agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz-like condition. Numerical examples are given to verify our proposed protocols.[23] and [24] designed continuous robust consensus tracking control laws for a class of first-order and second-order integrator-type multi-agents systems, respectively. Meng et al. designed both full state consensus protocol and dynamic output consensus protocols for a group of heterogeneous second-order nonlinear systems with bounded external disturbances in [25]. Hu et al. proposed a connectivity-preserving adaptive controller for a class of second-order multi-agents governed by locally Lipschitz nonlinearity in [26]. It should be pointed out that the control gains developed in [22][23][24][25] depended on the initial conditions of all agents. Therefore, only locally consensus could be guaranteed.Note that the control protocols constructed in [6-10, 14-17, 19-25] depended on the entire communication graph, such as the general algebraic connectivity of the information-exchange matrix. However, this is global information, which, in general, is not available to each agent. Therefore, those protocols cannot be implemented using only the local relative information between its own and its neighbors. To deal with this problem, [11][12][13] proposed both state-feedback and dynamic output-feedback adaptive consensus protocols for general linear multi-agent systems without using any global information. Yu et al. [18] designed adaptive control gains for second-order multi-agent systems with globally Lipschitz nonlinear dynamics under undirected communication topology. In our prior work [27] and [28], a distributed adaptive leader-following consensus protocol was constructed for a class of integrator-type nonlinear multi-agent systems under directed communication topology.In this paper, we study the robust consensus tracking problem for a class of heterogeneous second-order nonlinear multi-agent systems with external disturbances. When the full relative state information is available for feedback, a state-feedback distributed adaptive control law is constructed for the time-varying leader agent and external disturbances with unknown upper bound. When the relative velocity information is not available and only the relative position information is avai...
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