Fast funnel control based fixed-time consensus tracking for nonlinear multi-agent systems with unknown disturbances

This paper proposes a fixed-time consensus tracking control strategy for nonlinear multi-agent systems (NMASs) under unknown lumped disturbances, including internal system uncertainties and external disturbances. To address these challenges, a fixed-time sliding mode disturbance observer (FTSMDO) is designed. An auxiliary error dynamic system with fixed-time convergence is introduced for the sliding mode surface to achieve rapid and accurate disturbance estimation. Subsequently, a fast nonsingular funnel error surface (FNFES) with a hyperbolic tangent error transformation is proposed, effectively avoiding singularity while limiting the consensus tracking error within the performance funnel region. By integrating the FNFES into the backstepping control framework, a fast funnel controller is designed, which ensures the consensus tracking errors of NMASs converge to a prescribed boundary with small steady-state error, fast convergence, and reduced overshoot. Furthermore, an improved nonlinear filter with a coupling suppression term is designed to address the "explosion of complexity" (EOC) issue from the backstepping method and reduce controller conservativeness. The semi-global practical fixed-time stability (SPFS) of the closed-loop system is established via Lyapunov theory. Comparative simulations demonstrate the superiority of the proposed control strategy.