Analysis and Design of Interval Type-2 Polynomial-Fuzzy-Model-Based Networked Tracking Control Systems

Abstract

Highly nonlinear systems exist in many real-world applications. The control design of such systems is challenging even for existing advanced control theory. Besides, when there is uncertainty in the nonlinear system and networked control strategy is considered, the problem will become even more complicated. To confront the problem, for the first time, this article provides a solution for the tracking control design of the nonlinear networked control systems (NCSs) subject to uncertainty under the polynomial event-triggered mechanism (PETM). In the proposed tracking control scheme, the nonlinearity in the NCSs is effectively represented by a polynomial fuzzy model while the uncertainty is handled by the interval type-2 (IT2) fuzzy sets. The tracking control objective is to properly design the event-triggered IT2 polynomial controller, which drives the states of the plant to track those of the stable reference system under the PETM. Different from the existing works in the literature, the event-triggering condition can be varied according to the state to improve the flexibility and capacity of event-triggered mechanism. Furthermore, in some works reported in the literature, the perfect match of premise variables is assumed. However, this assumption is extremely difficult to be fulfilled in the event-triggered control applications. To address the long-standing challenge of an intrinsic mismatch issue of the premise variables due to event-triggering mechanism, in the proposed analysis, the imperfect premise matching (IPM) concept is adopted along with the membership-function-dependent (MFD) approach to facilitate the stability analysis and control synthesis. The stability conditions are summarized as sum-of-squares (SOS). The H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> index is utilized to evaluate the tracking control performance, and the performance can be improved through minimizing the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> index. A detailed simulation example is provided to verify the effectiveness of the proposed method.