Fixed-time consensus disturbance rejection for high-order nonlinear multi-agent systems with input saturation

This study is devoted to investigating the fixed-time consensus disturbance rejection problem for a class of high-order nonlinear multi-agent systems (MASs) with input saturation. A distributed fixed-time state observer (FTSO) is first proposed to reconstruct the leader's states for each follower. Based on the estimated values, a fixed-time consensus protocol is designed via backstepping, where a fixed-time disturbance observer (FTDO) is used to provide the robustness against the external disturbances. The violation of the input saturation is prevented by introducing an auxiliary variable and the problem of "explosion of terms" suffered by the conventional backstepping design is also successfully avoided by a fixed-time differentiator. Detailed convergence results are presented by leveraging Lyapunov stability theory. Finally, the effectiveness of the proposed approach is numerically validated through simulation results.