Linearized Bregman iteration based model‐free adaptive sliding mode control for a class of non‐linear systems

There is a growing demand for robust data‐driven control methods particularly for industrial process control. This paper presents a new model‐free adaptive sliding mode control approach for a class of discrete‐time, multiple input and multiple output non‐linear systems. The proposed methodology seeks to address issues with the computation of inverse matrices and problems with singularity in existing methods while at the same time seeking to enhance robustness. A Majorization–Minimization technique and the L1 norm are used within the proposed optimization and an online iterative approach is described for update of the control law. The closed‐loop system response is proved to be stable. The effectiveness of the proposed control is validated by extensive simulation and also experimental results, with the performance obtained by the proposed approach being compared throughout with a well‐known approach from the established literature.