Discrete-time extended state observer-based model-free adaptive sliding mode control with prescribed performance

To tackle the trajectory tracking problem and achieve high control accuracy in many actual nonlinear systems with unknown disturbance, a novel discrete-time extended state observer- (DESO) based model-free adaptive sliding mode control strategy with prescribed tracking performance is studied, which only relies on the input/output data of the system rather than explicit model information. Firstly, a compact-form dynamic linearization method is used to reconstruct the discrete-time nonlinear process, where the time-varying parameter linearly connected with the control input is obtained by an adaptive method and the unknown nonlinear term is estimated by a DESO. Then, by considering the prescribed performance and using an unconstrained vector transformed from the constrained tracking error, one model-free sliding mode controller is designed. In addition, a rigorous stability analysis is presented to show the boundedness of the sliding mode function and the prescribed transient-state and steady-state performance of the output tracking error. Finally, the simulations with comparing results verify the effectiveness and superiority of the developed control scheme.