Predefined-time smooth consensus of nonlinear multi-agent systems with undirected and directed graphs

This study addresses the predefined-time leader-following consensus problems for nonlinear multi-agent systems (MASs) under both undirected and directed topologies, respectively. The key contribution lies in the proposed differentiable consensus control protocols, which eliminate chattering by avoiding discontinuous absolute value and sign functions-overcoming a limitation of traditional designs. A critical advantage is that the upper bound of the settling time for predefined-time consensus (PTC) is an explicit, adjustable constant, preassignable without dependence on network topology, initial states, or system parameters, distinguishing it from finite-time or fixed-time paradigms. Using multi-layer communication networks and Lyapunov stability analysis, two sets of sufficient conditions are derived to ensure global PTC for the MASs. Numerical simulations with the Kuramoto model validate the theoretical results.