Prescribed-Time Output-Feedback Consensus of Nonlinear Multi-Agent Systems with Mismatched Uncertainties via Active Disturbance Rejection Control

This brief investigates the prescribed-time output-feedback consensus problem for a class of nonlinear multi-agent systems (MASs) subject to mismatched uncertainties and external disturbances. The key challenge lies in designing a low-complexity distributed protocol that achieves exact consensus within a user-assignable time, without relying on full-state measurements or conventional state transformations that impose restrictive differentiability conditions. To address this challenge, we propose a novel prescribed-time active disturbance rejection control (ADRC) scheme that integrates a prescribed-time extended state observer (PTESO) with a backstepping-based consensus protocol. The PTESO simultaneously estimates the unmeasured states and disturbances to achieve feedforward compensation, while the backstepping controller avoids reformulating mismatched terms into the input channel. By employing the homogeneous domination technique, both the tracking errors and the observer estimation errors are rigorously shown to converge to zero within the prescribed time. Numerical simulations validate the effectiveness and practical applicability of the proposed method in a networked control scenario.