Data-driven sliding mode control of unknown MIMO nonlinear discrete-time systems with moving PID sliding surface

Abstract This paper investigates the problem of data-driven sliding mode control (DDSMC) for a class of unknown MIMO nonlinear discrete-time systems with both uncertainties and disturbances. Utilizing the non-parametric dynamic linearization technique (NDLT) and the second-order discrete sliding mode observer (2-DSMO), a novel DDSMC law based on the PID sliding surface is developed to achieve faster transient responses with less steady-state tracking errors. A disadvantage of this strategy is that the PID sliding surface design is based on constant coefficients, which may prevent further control performance improvement of the plant. Then, inspired by the fuzzy logic control (FLC) scheme, a moving PID sliding surface is proposed to further enhance the performance of the DDSMC approach, where the PID sliding surface parameters are updated by the proposed data-driven adaptive law. Using the proposed sliding surface, faster dynamic response and less overshoot of the tracking behaviors are achieved with the magnitude of the discontinuous control gain unchanged. Furthermore, the couplings, uncertainties and disturbances are also suppressed owing to the application of the 2-DSMO. Also, the overall closed-loop system is also shown to be asymptotically stable. Finally, numerical and experimental results are given to validate the effectiveness of the proposed approach.