Stability-constrained adaptive recurrent network with fractional memory for lithium-ion battery state-of-health prediction

To overcome the limitations of standard gated recurrent units (GRUs) in capturing long-term degradation dependencies for lithium-ion battery state-of-health (SOH) prediction, as well as the fact that existing fractional recurrent models often rely on empirically selected orders and lack explicit stability constraints, this paper proposes an adaptive Grünwald-Letnikov (GL) fractional GRU model with convergence constraints. The proposed model embeds the GL fractional difference into the GRU hidden-state update process, thereby introducing nonlocal historical memory to enhance the representation of long-term degradation evolution. On this basis, the convergence condition for the fractional hidden-state recursion is derived, and gate-dependent sufficient bounds on the fractional order are derived as functions of the truncation length and the instantaneous update-gate value. Accordingly, a layer-wise adaptive order learning strategy with convergence-margin constraints is developed. The proposed method achieves the lowest MAE and RMSE of 0.183% and 0.313%, respectively, on the NASA dataset under the leave-one-battery-out evaluation. Meanwhile, it also demonstrates superior overall performance on the TJU dataset under cross-temperature and cross-rate distribution shifts. Comprehensive analyses confirm that the proposed model offers clear advantages in prediction accuracy, stability, and computational efficiency, providing a theoretically grounded and computationally compact framework for cycle-level one-step-ahead SOH prediction.