Prescribed‐Time Hierarchical Control for Nonlinear Multi‐Agent Systems

ABSTRACT This paper proposes the fully distributed observer‐based prescribed‐time (PT) distributed adaptive control strategy for high‐order uncertain nonlinear multi‐agent systems (MASs) with the time‐varying reference signal. Facing the main challenge that only the upper bound of order derivative and the first order derivatives of the reference signal are available for agents that directly communicate with it, a hierarchical control framework is built. In the estimated layer, a novel distributed estimator with the PT method is first designed to estimate the upper bound of the order derivative of the reference signal, which can achieve the PT convergence. By using the estimated value, a PT fully distributed observer in the observed layer is proposed to observe each order derivative of the reference signal, which can not only remove the limitation of the smallest nonzero eigenvalue of the Laplacian matrix related to the network topology but also make the observer error converge to zero at the given prescribed time. Based on this, the PT distributed adaptive controller is designed in the control layer by the back‐stepping method, which can realize the PT stabilization for the output tracking control. Finally, the effectiveness of the proposed control strategy is successfully verified by solving the power sharing for AC microgrids via a comparison.