Koopman-Based State-of-Charge Observer Design for Lithium-Ion Batteries: An LMI-Based Framework

Abstract This paper proposes a Koopman-based state-of-charge (SOC) observer for lithiumion batteries designed in a lifted linear space identified via extended dynamic mode decomposition with control (EDMDc). Accurate SOC estimation still remains challenging, since battery electrochemical dynamics are highly nonlinear and the SOC cannot be directly measured. To capture the intrinsic nonlinear characteristics of battery dynamics, we construct a physicsinformed dictionary of observable functions defined over the battery state variables. Based on the resulting Koopman linear representation, battery SOC observers are developed via linear matrix inequalities (LMIs), ensuring the stability of the estimation error dynamics in the lifted space. Finally, the proposed framework is validated using multiple battery datasets under various dynamic loading conditions. The proposed observer achieves root mean square errors (RMSE) between 0.0214 and 0.0248 across different driving profiles, demonstrating significantly improved SOC estimation performance compared with an extended Kalman filter (EKF)-based approach (RMSE: 0.0401–0.0505), which has been widely used in the battery community.