Operator-Theoretic Joint Estimation of Aging-Aware State of Charge and Control-Informed State of Health

Abstract: Accurate estimation of a battery's state of charge and state of health is essential for safe and reliable battery management. Existing approaches often decouple these two states, lack stability guarantees, and exhibit limited generalization across operating conditions. This study introduces a unified operator-theoretic framework for aging-aware state of charge and control-informed state of health estimation. The architecture couples a Koopman-based latent dynamics model, which enables linear forecasting of nonlinear discharge-capacity evolution under varying operational conditions, with a neural operator that maps measurable intra-cycle signals to state of charge. The predicted discharge capacity is incorporated as a static correction within the neural operator pathway, yielding an age-aware state of charge estimate. Stability is ensured through spectral-radius clipping of the Koopman operator. The overall framework is trained end-to-end and evaluated on real-world lithium-ion battery datasets, demonstrating real-time capability while maintaining stable dynamics. To handle condition shifts and unseen regimes, the method integrates both zero-shot and few-shot out-of-distribution adaptation using only a limited number of cycles. Results show accurate and stable capacity forecasts, competitive state of charge trajectories on held-out cycles, and a direct, model-consistent mechanism for tracking capacity fade as a surrogate for state of health across diverse operating conditions.