Variable Universe Fuzzy Control Based on Adaptive Error Integral for Uncertain Nonlinear Systems with Time-Delay

This article deals with variable universe fuzzy control (VUFC) based on adaptive error integral for uncertain nonlinear systems with time delay. A novel fuzzy control strategy is firstly addressed for the system to guarantee asymptotic stability. The strategy concludes in three modules: first, introduced an extended state observer to observe the extended state variables and estimate the unknown total disturbance and the unmodeled dynamics of the controlled plant; second, employ a tracking differentiator to track the dynamic characteristics of the input signal as quickly as possible in the strategy; and thirdly, develop a variable universe fuzzy control for the external-loop system with the observer and the differentiator. Compared with the existing results, the proposed strategy relaxes the restrictions on the conventional domain by the self-regulation of the tracking error domain during the operation of the system. Furthermore, to enhance the control accuracy of the controller, we define an extended adaptive error integral which can not only remain superior to the traditional error integral but also overcome the inferior. In addition, the boundedness of all signals of the presented systems is analyzed and proved by the Lyapunov theory. In the end, several simulation examples and some comparisons are presented to highlight the novelty and feasibility of the proposed method.