Novel Fractional-Order ESO-Based Distributed Control for Multi-Agent Systems to Pass a Curve Virtual Tube with Matched and Mismatched Disturbances

To guide multi-agent systems (MASs) through a cluttered environment, this paper proposes a distributed control method based on a novel fractional-order extended state observer (NFO-ESO). First, unlike the traditional multi-agent double-integral model, the agent model constructed in this paper contains external wind disturbances (mismatched disturbances) and internal unmodeled dynamics (matched disturbances), and these disturbances are treated as matched disturbance equivalent. Then, the designed disturbance observer is added to the robust distributed controller to coordinate the disturbance, which is used to accomplish the curve virtual tube crossing task in the perturbed case. The disturbance observer is NFO-ESO, which is implemented in this paper by constructing a neural network based on fractional-order discrete theory. It improves the weakness of the traditional ESO that only observes low-frequency slow time-varying disturbances and can be more suitable for nonlinear fast time-varying disturbance estimation. Finally, to demonstrate the advantages of the proposed controller, we show an example of MASs with wind disturbance and unmodeled dynamic through numerical simulation experiment. The instance shows the effectiveness of the proposed distributed control method under external disturbances.