Distributed extended state observer design for strict-feedback nonlinear leader system

Knowing the leader's state and dynamics is crucial for leader-following control. This article addresses the distributed state/uncertainty estimation problem for a strict-feedback nonlinear leader system under directed communication topologies. The leader is characterized by Hölder-growing nonlinearities and matched uncertainty. A prescribed-time distributed estimation scheme composed of two distributed extended state observers (DESOs) is proposed. Each follower (observer node) receives only one-dimensional output estimates from its neighbors and at most one-dimensional output from the leader system, effectively reducing the communication load. First, a prescribed-time DESO (PTDESO) is proposed so that each follower can reconstruct the leader's state and uncertainty at a time tightly prescribed by a single parameter, uniform to the initial conditions. Then, a high-gain DESO (HGDESO) is constructed, which achieves asymptotic convergence and maintains the observation errors in a small neighborhood of the origin after the prescribed time. Sufficient conditions for guaranteeing the convergence of the two DESOs are established. Ultimately, practical examples involving multiple manipulators and marine surface vehicles are provided to demonstrate the effectiveness of the proposed observers.