Secure Estimation of Battery Voltage Under Sensor Attacks: A Self-Learning Koopman Approach

A cloud-based battery management system (BMS) requires accurate terminal voltage measurement data to ensure optimal and safe charging of Lithium-ion batteries. Unfortunately, an adversary can corrupt the battery terminal voltage data as it passes from the local-BMS to the cloud-BMS through the communication network, with the objective of under- or over-charging the battery. To ensure accurate terminal voltage data under such malicious sensor attacks, this paper investigates a Koopman-based secure terminal voltage estimation scheme using a two-stage error-compensated selflearning feedback. During the first stage of error correction, the potential Koopman prediction error is estimated to compensate for the error accumulation due to the linear approximation of the Koopman operator. The second stage of error compensation aims to recover the error amassing from the higher-order dynamics of the Lithium-ion batteries missed by the selflearning strategy. Specifically, we have proposed two different methods for this second stage error compensation. First, an interpretable empirical correction strategy has been obtained using the open circuit voltage to state-of-charge mapping for the battery. Second, a Gaussian process regression-based datadriven method has been explored. Finally, we demonstrate the efficacy of the proposed secure estimator using both empirical and data-driven corrections.