Passivity and synchronization of fractional-order coupled neural networks with multiple weights: A PD approach.

Traditional control methods for complex neural networks are constrained by their dependence on precise models, neglecting the robustness needed to address high-dimensional coupling characteristics and model uncertainty, which usually results in inflexible responses to disturbances. This paper explores the passivity and synchronization of fractional-order coupled neural networks with multiple weights (FOCNNMWs) using a designed proportional-derivative (PD) control strategy. On one hand, the analysis of various passivity properties in FOCNNMWs, including input-strictly passivity and output-strictly passivity, is conducted through PD controllers, Lyapunov functions, and linear matrix inequality method; on the other hand, a sufficient condition for synchronization is derived by means of output-strictly passivity, utilizing both energy function analysis and the limit properties of Mittag-Leffler function. The proposed PD control approach, via passivity-based analysis, not only avoids the requirement for precise modeling of nonlinear terms but also inherently resists disturbances through passivity's energy dissipation, curbing its impact on synchronization errors. Finally, numerical simulations with two distinct cases confirm the effectiveness of the proposed criteria.