Data-driven integral sliding mode predictive control with optimal disturbance observer

In this paper, a novel data-driven integral sliding mode predictive control algorithm based on an optimal disturbance observer (DDISMPC-ODO) is proposed for a class of nonlinear discrete-time systems (NDTS) subject to external disturbances. The designed optimal disturbance observer realizes the precise observation of the lumped disturbance, thus ameliorating the accuracy of the controller and weakening problems with chattering. In this work, a robust pseudo-partial derivative (PPD) estimation algorithm is introduced, which not only improves the system performance, but also facilitates theoretical proof of parameter estimation and tracking accuracy. The convergence of the PPD estimation error and disturbance observation error is proved. It is also proved that the accuracy of the disturbance observation error can converge to $O\left(T^3\right)$ and then the magnitude of the sliding variable and the tracking error are also reduced to $O\left(T^3\right)$ respectively. Finally, the effectiveness of the proposed method is demonstrated by a simulation example and an experiment.