<i>H</i> _∞ Controller Synthesis for IT2 Fuzzy Systems via Membership Function Optimizer and Enhanced Dynamic Event-Triggered Mechanisms

This article addresses the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> control problem for networked interval type-2 (IT2) fuzzy systems under limited communication resources. To improve efficiency and robustness, a novel dual-channel event-triggered mechanism (ETM) is developed to reduce redundant data transmissions. Furthermore, a dynamic memory-based ETM (DMETM) is proposed, where traditional static error coefficients are replaced with system-dependent dynamic coefficients, constructed using historical triggering data. This reduces conservatism and ensures better adaptability during transient and steady-state phases, while effectively avoiding Zeno behavior. To tackle the membership function (MF) mismatch problem caused by event-triggered (ET) transmissions, equations incorporating MF information are introduced to establish connections between mismatched MFs. A real-time gray wolf optimizer (GWO)-based strategy, enhanced with local search techniques, is introduced to automatically optimize the controller’s MF parameters, thus overcoming the limitations of manual, experience-based MF design. Compared to conventional controllers relying on expert subjective knowledge or intuition, this method offers superior transient performance and tolerance to unmodeled errors in the system. Simulation results confirm that the proposed approach achieves superior performance in terms of transient behavior, disturbance attenuation, and resource conservation compared to conventional methods. The proposed framework offers a practical and scalable solution for IT2 fuzzy controller design in resource-constrained networked systems.