This paper investigates the problem of finite-time consensus tracking for a class of multiple uncertain mechanical systems under switching topologies. In the presence of uncertainties and input saturations, a distributed observer-based adaptive finite-time tracking protocol is proposed. At the first step, a distributed observer is proposed for each mechanical system to observe the leader's state in finite time; then, an adaptive finite-time tracking protocol is designed to track the estimated state via recursive design method. Neural networks are used to approximate the unknown continuous functions. It is proved that under the designed protocol, the consensus tracking of position and velocity can be achieved in finite time. Finally, an example is given to demonstrate the effectiveness of the proposed method.M. CAI AND Z. XIANG ing has also been well studied [15][16][17] because load balancing is a fundamental requirement of many networked systems like distributed computing systems, grid systems, and wireless networks. Although consensus issue has attracted much attention, there still exist many research opportunities in both theoretical and practical aspects.In consensus problem of multi-agent systems, finite-time consensus is one particular area of interest for its faster convergence and high performances, such as better disturbance rejection and robustness against uncertainties [18,19]. In the field of finite-time consensus, model uncertainties including unknown parameters and unmodeled dynamics have become a new issue because uncertainties inevitably exist in almost all the practical multi-agent systems. In [20], the finite-time consensus problem of leader-follower systems with leader having unknown nonlinear control input signal and followers having unknown nonlinear dynamics was considered, where the unknown nonlinear dynamics were assumed to be Lipschitz continuous and can be linearly parameterized. In [21], the finite-time consensus problem for leader-follower high-order uncertain nonlinear systems was considered, in which the nonlinearities were assumed to be partially unknown and the unknown part together with the input disturbance were assumed to have a known bound, which can be directly used in the designed controller. The finite-time consensus control for first-order multi-agent systems with unknown inherent nonlinear dynamics was studied in [22], where the unknown nonlinearity of the agent dynamics was assumed to satisfy Lipschitz condition and the Lipschitz coefficient was assumed to be known. In [23] and [24], efforts have been made by using adaptive method in addressing finite-time consensus for multiple mechanical systems with model uncertainties. However, it is worth noting that the uncertainties considered in both [23] and [24] were assumed to exhibit the linear parametric property; without such property, the adaptive methods for finite-time consensus were inapplicable. Recently, the finite-time consensus control for multiple uncertain mechanical systems with undetectable actuator faults was r...
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