Backstepping active disturbance rejection control: a delayed activation approach

This study provides a solution to the problem of applying the active disturbance rejection control (ADRC) approach to the tracking control of pure feedback non-linear systems with large uncertainties. The design is based on the backstepping technique, and in each step two extended state observers (ESOs) are designed, one to approximate the derivative of the virtual control generated from the last step, while the other to estimate the system uncertainty. A key feature of the developed backstepping ADRC is that the activations of the ESOs are delayed successively. It is proved that under the new backstepping scheme, the closed-loop signals are guaranteed to be semi-globally uniformly ultimately bounded and the output tracking error can be made arbitrarily small.