Adaptive Fuzzy Control of a Class of Discrete-Time Nonlinear Systems

This paper presents a data-driven adaptive fuzzy control (DDAFC) method for a class of unknown discrete-time non-linear systems. First a virtual data-driven controller is derived via a dynamic linearization technique, which is in the dynamically incremental form with the so-called pseudo-partial derivative (PPD). Then the virtual data-driven controller is represented by a fuzzy model with the PPD vector being approximated, where the fuzzy weights are tuned online via the input-output data of the closed-loop control system. The stability analysis shows that the fuzzy adaptive controller can force the original unknown nonlinear system to track the reference signal with a uniformly ultimately bounded tracking error, and besides, the fuzzy weights, the PPD estimate of the plant, and the control input are all bounded. The advantage and effectiveness of the proposed method are shown by the numerical simulation example.