Adaptive Event-Triggered Control for Limited-Time Bipartite Synchronization of T–S Fuzzy Memristive Neural Networks and Applications for PCMS

This article investigates the limited-time bipartite synchronization (LTBS) problem of coupled T-S fuzzy memristive neural networks (CTSFMNNs) with antagonistic interactions, where LTBS covers both fixed-time bipartite synchronization (FXTBS) and preassigned-time bipartite synchronization (PATBS). To address this issue, a fuzzy exponential control strategy is developed based on an improved adaptive event-triggered mechanism (IAETM). By employing constant gains and exponential terms instead of conventional switching gains and multiple power-law structures, the controller design is simplified and its implementability is enhanced. Furthermore, an adaptive function and two dynamic regulation terms are incorporated into the ETMs to adjust the triggering threshold according to measurement-error variations, thereby reducing controller updates and conserving communication resources. Then, algebraic inequality criteria are established through Lyapunov theory and the fuzzy set method to guarantee the LTBS of CTSFMNNs. Finally, numerical simulations are conducted to verify both the effectiveness of the derived synchronization conditions and the feasibility of an image data protection framework for Pantograph-Catenary Monitoring System (PCMS) constructed from the obtained LTBS theory. The proposed framework provides controllable key-generation time, a decoupled design of the key and the synchronous sequence, and enhanced resistance to structure-inference attacks, thereby improving security and demonstrating strong engineering potential.