Backstepping Active Disturbance Rejection Control for Lower Triangular Nonlinear Systems With Mismatched Stochastic Disturbances

In this article, we apply the active disturbance rejection control (ADRC) to the output tracking of a class of lower triangular nonlinear systems subject to mismatched bounded stochastic disturbances of unknown statistic characteristics and nonvanishing at the origin. A major obstacle is that the paths of the stochastic disturbances are nowhere differentiable almost surely which causes that the stochastic disturbances cannot be refined into the control input channel by the usual way of state transformation. To overcome this obstacle, a set of second-order extended state observers is first designed to estimate, in real time, the disturbance in each channel, and then a backstepping ADRC based on feedforward compensation and a constructive backstepping procedure is developed, guaranteeing that the closed-loop output tracks a time-varying reference signal in practically mean square and the closed-loop states are practically bounded in probability first defined in this article. Finally, some numerical simulations are presented to validate the effectiveness of the proposed backstepping ADRC approach.