Learning‐Based Formation Control of Distributed MASs With Actuator Hysteresis Using Graph Convolutional Networks

This paper investigates distributed time‐varying formation control for second‐order nonlinear multi‐agent systems (MASs) subject to Bouc Wen actuator hysteresis and unknown disturbances. A graph convolutional network (GCN) is integrated as a topology‐aware local estimator of unknown nonlinear disturbances, and combined with dynamic sliding mode control (DSMC) to preserve robustness and suppress chattering, leading to a GCN DSMC framework. A Chebyshev‐polynomial spectral GCN is adopted to reduce the computational burden while retaining graph‐structured uncertainty estimation. Lyapunov‐based analysis shows that all closed‐loop signals are bounded and the formation‐tracking errors are uniformly ultimately bounded. Simulations are conducted from three aspects: formation tracking under different topologies and team sizes, comparative evaluation against DSMC and RBFNN DSMC baselines, and computational scalability analysis. The results demonstrate the advantages of the proposed method in tracking accuracy, robustness, topology adaptability, and computational efficiency.