Self-Adaptive Neural Network-Based Fractional-Order Nonlinear Observer Design for State of Charge Estimation of Lithium-Ion Batteries

Accurate state of charge (SOC) estimation provides an essential basis for the functionalities of battery management systems in electric vehicles (EVs). However, conventional equivalent circuit models suffer significant model accuracy deterioration under extreme SOCs, nonroom temperatures, and heavy loads. In this work, we implant the Butler–Volmer (BV) equation and the fractional-order model representation into a model-based physics-informed neural network (M-PINN) to simulate current-dependent battery charge transfer dynamics under various operating conditions. This M-PINN replaces the original neuron structure with a set of submodels and allows the BV coefficient to be randomly selected in a roughly estimated range for each submodel. By applying the Lyapunov analysis, a self-adaptive neural network-based fractional-order observer is proposed to guarantee the uniform ultimate boundedness stability of both system states and M-PINN weights, thereby achieving accurate online SOC estimation without necessitating substantial data and efforts for offline neural network training. The experimental validations are implemented under three EV driving profiles with different average currents at −5, 5, 20, and 35 Celsius. The validation results demonstrate that the proposed method achieves the mean absolute errors of less than 0.9% in all the validation scenarios.