Abstract
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.
Highlights
In modern control theory, the design of the controller is frequently carried out using a mathematical model
The purpose of this study is to design a novel Model-free adaptive sliding mode control (MFASMC) for a class of multiple input multiple output (MIMO) nonlinear discrete-time systems where the model is unknown based on linear Bregman iteration [19]
The main contributions of this study are summarized as follows: (i) the Majorization–Minimization (MM) principle is used in optimizing the objective function, which avoids the computational time increase caused by matrix inversion; (ii) an L1 norm term is used in the control input criterion function and the linear Bregman algorithm is employed for the solution, which can enhance the system robustness
Summary
The design of the controller is frequently carried out using a mathematical model. The study of discrete-time SMC has facilitated the integration of sliding mode techniques with industrial computer systems [14, 15] These studies mainly focus on the development of adaptive model-based controllers. Model-free adaptive sliding mode control (MFASMC) is proposed in [16] for single input and single output non-linear discrete systems. The purpose of this study is to design a novel MFASMC for a class of MIMO nonlinear discrete-time systems where the model is unknown based on linear Bregman iteration [19]. The main contributions of this study are summarized as follows: (i) the Majorization–Minimization (MM) principle is used in optimizing the objective function, which avoids the computational time increase caused by matrix inversion; (ii) an L1 norm term is used in the control input criterion function and the linear Bregman algorithm is employed for the solution, which can enhance the system robustness.
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