Adaptive neural network‐based practical fixed‐time consensus tracking for second‐order nonlinear multi‐agent systems with switching topologies

Abstract The current study concerns the practical fixed‐time consensus tracking problem of second‐order nonlinear multi‐agent systems (MASs) with switching topologies. The neural network (NN) and adaptive technique are adopted to compensate the unknown nonlinearities of the followers. Then, an adaptive NN‐based fixed‐time controller is designed under switching interaction topologies. In order to give the rigorous proof of the practical fixed‐time consensus tracking, a novel lemma for analyzing the practical fixed‐time stability of the switched error system is firstly established, then by constructing appropriate topology‐dependent multiple Lyapunov functions, we theoretically show that the practical fixed‐time consensus tracking of the closed‐loop MASs can be ensured provided that the dwell time of the switching topologies is larger than a predefined threshold and further the involved control parameters are suitably selected. Moreover, the settling time estimation is explicitly given, which is regardless of the system's initial values. The theoretical results are finally verified via a numerical simulation.