Adaptive Sliding Mode Decoupling Control with Data-Driven Sliding Surface for Unknown MIMO Nonlinear Discrete Systems

This paper investigates the second-order sliding mode control (2-SMC) problem for a class of unknown multi-input multi-output nonlinear discrete systems. First, by nonparametric dynamic linearization technique and the extended state observer, a novel data-driven sliding surface is designed that can establish the relation between the desired trajectories and the control inputs. An adaptive 2-SMC law based on the proposed sliding surface is then derived to deal with the effects of couplings, uncertainties and external disturbances. Using the proposed sliding surface, a better decoupling ability and stronger robustness of the proposed approach are achieved. In addition, it is proved that the states of closed-loop system are asymptotically stable. Finally, an example of three-tank system is given to demonstrate the effectiveness of the theoretical results.