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This paper presents a robust sliding-mode observer (RSMO) for state-of-charge (SOC) estimation of a lithium-polymer battery (LiPB) in electric vehicles (EVs). A radial basis function (RBF) neural network (NN) is employed to adaptively learn an upper bound of system uncertainty. The switching gain of the RSMO is adjusted based on the learned upper bound to achieve asymptotic error convergence of the SOC estimation. A battery equivalent circuit model (BECM) is constructed for battery modeling, and its BECM is identified in real time by using a forgetting-factor recursive least squares (FFRLS) algorithm. The experiments under the discharge current profiles based on EV driving cycles are conducted on the LiPB to validate the effectiveness and accuracy of the proposed framework for the SOC estimation. [ABSTRACT FROM AUTHOR]