Decomposition for Large-Scale Optimization Problems: An Overview

This paper explores the issue of secure synchronization control in piecewise-homogeneous Markovian jump delay neural networks affected by denial-of-service (DoS) attacks. Initially, a novel memory-based adaptive event-triggered mechanism (MBAETM) is designed based on sequential growth rates, focusing on event-triggered conditions and thresholds. Subsequently, from the perspective of defenders, non-periodic DoS attacks are re-characterized, and a model of irregular DoS attacks with cyclic fluctuations within time series is further introduced to enhance the system's defense capabilities more effectively. Additionally, considering the unified demands of network security and communication efficiency, a resilient memory-based adaptive event-triggered mechanism (RMBAETM) is proposed. A unified Lyapunov-Krasovskii functional is then constructed, incorporating a loop functional to thoroughly consider information at trigger moments. The master-slave system achieves synchronization through the application of linear matrix inequality techniques. Finally, the proposed methods' effectiveness and superiority are confirmed through four numerical simulation examples.