**3. ANFIS Li-ion battery model design for dynamic part Rint-3RC ECM and OCV(SOC) nonlinear block**

As an alternative to 3RC ECM and ARX battery models, the ANFIS modeling techniques are based on specific MATLAB commands provided by fuzzy logic toolbox and based on fuzzy inference tuning procedures [14–16]. The Sugeno-type inference system FIS is tuned based on an input-output training data set collected in open-loop from 3RC ECM Li-ion battery model. From our most recent preliminary results in the Li-ion battery field, modeling and SOC estimators disseminated in [12, 25, 26], an interesting state-of-the-art analysis of similar SOC AEKF estimators performance reported in the literature is done in terms of statistical performance criteria values, such as root mean square error (RMSE), mean square error (MSE), mean absolute error (MAE), standard deviation (std), mean fundamental percentage error (MAPE), and R2 (R-squared). Among three SOC Li-ion battery estimators, the AEKF, adaptive unscented Kalman filter (AUKF), and particle filter (PF) SOC estimators, the AEKF proved that is the most suitable for HEVs applications [29].

#### **3.1 Detailed ANFIS Li-ion battery model design steps**
