Prescribed-Time Active Disturbance Rejection Control for Nonlinear Systems With Mismatched Uncertainties: A Non-Separation Principle Approach

This paper addresses the problem of prescribed-time output feedback stabilization for a class of nonlinear uncertain systems with both external disturbances and mismatched uncertainties. By utilizing a non-separation principle design approach, a novel active disturbance rejection control (ADRC) scheme is proposed. Firstly, a prescribed-time extended state observer (PTESO) is designed to simultaneously estimate unmeasured system states and external disturbances. Secondly, a feedforward-feedback composite controller is developed by integrating the PTESO with a constructive backstepping procedure. Furthermore, the prescribed-time stability of the entire closed-loop system is rigorously analyzed by using a Lyapunov function method. Finally, numerical simulations validate the effectiveness of the proposed control method.