Data-Driven Adaptive Sliding-Mode Control based on Lyapunov theory for nonlinear MIMO systems with external disturbances

The model-based controllers need a mathematical model of the system, whereas the data-driven controllers operate based on measuring the input-output data. Nowadays, considering complexity of the industrial systems and unavailability of an accurate mathematical model of the system, scientists try to reduce dependency of the controllers on the mathematical model. In this paper, an adaptive sliding-mode data-driven controller for a class of unknown multi-input multi-output nonlinear discrete-time systems is proposed. Because the chattering phenomenon is the main challenge of the sliding-mode controllers, an adaptive sliding-mode controller is used to solve this problem. In addition, to solve the dependencies of the controller on the mathematical model, the proposed adaptive sliding-mode controller is combined with a data-driven controller. Next, the new adaptive laws for the switching gain and the Pseudo Jacobian Matrix (PJM) are calculated. In addition, the closed-loop stability based on the Lyapunov theory is investigated. To show performance of the controller, the proposed method is applied to a three-tank system. The proposed controller has some advantages in comparison with similar methods in references, such as reducing the conservatism and complexity in the controller design and simplifying the closed-loop stability analysis. The simulated results show that the proposed method better tracks the reference signals and improves rejection of the external disturbances. Furthermore, the chattering phenomenon is considerably reduced.