Designing Pinning Control Synchronization Scheme for Inertial Memristive Neural Networks With Dynamic Granger Causality

Understanding the communication and information processing mechanisms in pinning control is highly influenced by the connectivity structure of the network, particularly in higher-order networks. However, existing studies predominantly focus on static network structures and utilize complete error information, often neglecting underlying inter-node dependencies, thereby limiting the effectiveness of low-energy control in higher-order dynamic systems. To address these limitations, this paper proposes a novel pinning control scheme for the synchronization of inertial memristive neural networks (IMNNs) based on dynamic Granger causality analysis (DGCA). First, an interpretable IMNN model is constructed to explicitly characterize higher-order interactions without decomposing the system into first-order subsystems. Then, unlike traditional pinned-node selection strategies relying on static interaction rules, a causality-aware selection algorithm is developed using DGCA to dynamically identify influential nodes via time-series analysis, enhancing control efficiency under dynamic network conditions. Furthermore, a local information-based pinning controller is designed by leveraging local causal relationships and control influence regions extracted from DGCA, ensuring the stability of the synchronization error system. Theoretical guarantees are provided by deriving sufficient conditions for controller design based on Lyapunov stability theory. Finally, three numerical examples are presented to demonstrate the effectiveness and practicality of the proposed scheme.