Distributed finite-time neuro-sliding mode control of high-order unknown heterogeneous nonlinear leader-following systems under unknown external disturbances

This study proposes a new distributed neuro-sliding control protocol to address the finite-time leader−follower tracking problem for a large class of high-order, unknown, heterogeneous nonlinear multi-agent systems (MASs) under unknown external disturbances. These systems are characterized by their sufficiently general forms, the presence of completely unknown nonlinear functions affecting the dynamics of all states, and the occurrence of unknown external disturbances. Furthermore, the dynamics of the leader node may differ from those of the follower nodes. In addition, we avoid imposing standard restrictive assumptions, such as Lipschitz continuity or bounded nonlinearities; instead, it suffices that the unknown nonlinearities be continuous. First, a sliding surface is proposed based on the total consensus error of all nodes. Second, radial basis function (RBF) neural networks are investigated to estimate the unknown nonlinear dynamics of both the followers and the leader. Next, a distributed neuro-sliding mode controller is designed to achieve finite-time consensus and accelerate the convergence of the MASs, even in the presence of unknown external disturbances. In addition, a Lyapunov equation is developed to demonstrate the finite-time stability of the proposed method. The proposed method provides several benefits, including the robustness of the consensus protocol, the rapid convergence of errors to zero, and the finite-time stability of the closed-loop system. The simulation results demonstrate the proposed method’s effective performance.