On Prescribed Performance ADRC for a Class of Nonlinear Systems with Uncertain Control Input Gain

This paper considers the prescribed performance tracking problem for nonlinear systems with uncertain control input gain. A novel prescribed performance active disturbance rejection control design featured with low computational complexity and large feasible range of the nominal control input gain is proposed. To deal with the tracking error constraint, an output error transformation is introduced to transform the constrained variable into an unconstrained one. A high-gain observer and sliding surface technique are combined to stabilize the converted unconstrained control system. To reduce the computational complexity, a reduced-order extended state observer is designed to estimate the system uncertainties and the high-order derivatives terms of error transformation, which arise from the ‘explosion of terms’. Moreover, compared with the existing prescribed performance ADRC, the proposed ADRC method needs only the control direction, relaxing the strong assumption on the nominal control input gain. It can be proved that the resulting closed-loop system is semi-globally uniformly ultimately bounded (SGUUB), which ensures the prescribed performance of the tracking error. Finally, simulation results demonstrate the effectiveness of the proposed control scheme.