Observer-Based Fixed-Time Consensus Control for Nonlinear Multi-Agent Systems Subjected to Measurement Noises

This article investigates the fixed-time consensus control problem for nonlinear second-order multi-agent systems subjected to measurement noises and in absence of the second-order state measurements of the leader and the followers under directed communication topology graphs. For each follower, an innovative augmented fixed-time disagreement error observer (AFTDEO) is first designed to reconstruct the disagreement error within fixed time. On one hand, the proposed AFTDEO can not only operate well only depending on the noisy measurements of the first-order states of the leader and the followers, but also suppress the measurement noises of the leader and the followers. On the other hand, the proposed AFTDEO can guarantee that the observation errors are convergent to the origin in fixed time independent of the initial observation errors. Based on the proposed AFTDEO, a novel fixed-time consensus control scheme under a directed graph having a spanning tree is constructed to address the consensus problem without the second-order measurements of the leader and the followers by utilizing fixed-time nonsmooth backstepping technique. The fixed-time convergence of the tracking error is guaranteed through Lyapunov stability analysis. Finally, simulation results demonstrate the effectiveness of the proposed consensus control scheme.