Improved approximation-free control for the leader–follower tracking of the multi-agent systems with disturbance and unknown nonlinearity

Approximation-free control effectively addresses uncertainty and disturbances without relying on approximation techniques such as fuzzy logic systems (FLS) and neural networks (NNs). However, singularity problems—where signals exceed preset boundaries under dynamic operating conditions—remain a challenge. This paper proposes an improved approximation-free control (I-AFC) method for the multi-agent system, which introduces a novel singularity compensator, providing a low-complexity design with exceptional adaptability while reducing the risk of singularity issues under changing working conditions (random initial values, system parameter variations, and changes in topology graph and followers’ dynamics). Furthermore, theoretical analysis guides parameter selection by demonstrating the method’s favorable convergence rate and appropriate control gain. Simulation results validate the approach.