Error-Based Model-Free Adaptive Performance Tuning Control With Disturbance Rejection for Discrete-Time Nonlinear Systems

This article proposes an error-based model-free adaptive performance tuning control (E-MFAPTC) strategy with disturbance rejection for a class of discrete-time nonlinear systems. First, the original discrete-time nonlinear system is converted into a novel tracking error-based compact form dynamic linearization (E-CFDL) model, which enables the parameter estimation algorithm, discrete-time extended state observer (DESO), and control law to be uniformly designed based on the tracking error. Consequently, the structure of the closed-loop system and adaptive controller is simplified. Then, a nonlinear proportional performance tuning function with desired constraints is proposed to adjust the tracking performance, and the strict constraints on tracking errors caused by barrier functions in discrete-time prescribed performance controls (PPCs) have been removed. Furthermore, to simplify the control structure under the introduced DESO, the lumped disturbance in the E-CFDL model is reconstructed, encompassing the desired tracking error, actual tracking error, and dynamic linearization (DL) error. Finally, theoretical analysis demonstrates that the parameter estimation algorithm, DESO, and tracking errors are all ultimately bounded, and the effectiveness of the proposed control strategy is verified via experimental results.