Nonsmooth funnel function-based model-free adaptive sliding-mode control for discrete-time nonlinear systems

This paper proposes a nonsmooth funnel function (NFF)-based model-free adaptive sliding-mode control strategy for the discrete-time nonlinear systems with unknown dynamics and asymmetric constraints. The dynamic linearization model of the nonlinear systems with unknown dynamics is obtained online only using the input/output data, which is combining with the designed NFF-based discrete-time sliding-mode surface to guarantee asymmetric constraints of the tracking error. In the proposed NFF, the coordinate transformation for asymmetric constraints simplifies the controller design, and the nonsmooth parameter can improve the transient and steady-state performances of the tracking error. The control consumption is further reduced by a proposed time-varying weighting factor-based cost function in the controller design. Furthermore, parameter selections of performance boundaries and the sliding-mode surface are given, and the performance margin (the minimum distance from the tracking error to the preset boundaries) is proved theoretically. Simulation and experimental results verify the effectiveness of the proposed control strategy.