Affine equivalent model based on data-driven fuzzy rules for a class of discrete-time adaptive controller

In this work, the affine equivalent model (AEM) is developed by using only the controlled systems's input-output data and it's relation based on fuzzy rules. Multi-input fuzzy rules emulated network (MiFREN) is used as function approximator when learning laws are designed to reduce the model error. Furthermore, AEM stability is guaranteed according to Lyapunov by theorem III.1. Thereafter, the control law is proposed with the information obtained by AEM. The tracking error resulted from the closed-loop system is proved as a convergent sequence by Lemma IV.1. The main advantage results in a simple control scheme and low computational cost. Numerical discrete-time systems (linear and nonlinear) are used to validate the performance of the proposed scheme altogether with the comparison results.