Switching Event-Triggered-Based Gain-Scheduled Control for Bipartite Synchronization of Coupled Coopetitive Memristive Neural Networks

This article investigates the problem of bipartite synchronization (BS) for coupled coopetitive memristive neural networks (MNNs) using a switching event-triggered gain-scheduled control strategy. First, a mathematical model of coupled MNNs exhibiting both cooperative and competitive interactions is formulated based on directed signed graph theory. To handle the antagonistic nature of these interactions, an orthogonal transformation is employed to develop a formally unified error system. Then, a switching event-triggered scheme (SETS) is designed, which leverages the coopetitive relationships among nodes to reduce communication costs. Meanwhile, a gain-scheduled controller, which incorporates the cooperative-competitive relationships is designed to achieve the BS. Specifically, the controller consists of both linear and nonlinear components: the linear component ensures system stability, while the nonlinear component compensates for residual terms arising from the heterogeneous structure of MNNs. Furthermore, the nonlinear control gains are scheduled via a function that depends on the error state, its derivative, and the sampled error, thereby reducing the conservatism of the synchronization conditions. A piecewise interval-dependent Lyapunov functional tailored to the characteristics of SETS is constructed. By employing inequality techniques, sufficient conditions for BS are derived in the form of linear matrix inequalities (LMIs), enabling the joint design of the linear control gains and the triggering matrix. To validate the proposed method, both a numerical example and a potential practical application are provided. In addition, two comparative studies are conducted to highlight the advantages of the proposed SETS and the interval-dependent Lyapunov functional, respectively.