Predefined‐Time Consensus Tracking for Second‐Order Nonlinear Multi‐Agent Systems Under External Disturbances

ABSTRACT This paper investigates the predefined‐time consensus tracking problem for second‐order nonlinear multi‐agent systems (MAS) under disturbance. Firstly, a predefined‐time observer is designed to estimate the state of the entire system, ensuring that the observed state and the leader state achieve consensus within a predefined time. Secondly, a nonsingular terminal sliding mode (NTSM) controller is designed to drive the tracking errors to zero exactly within a predefined time, effectively handling nonlinearities and disturbances without singularity. In this context, the convergence time is directly determined by tunable parameters, enabling the control protocol to satisfy specific design requirements. Using Lyapunov stability theory and predefined‐time stability theory, we rigorously derive sufficient conditions for predefined‐time consensus in disturbed second‐order nonlinear MAS. Furthermore, a numerical simulation is provided to demonstrate the validity and effectiveness of the proposed theoretical results.