Safe and reliable operation of lithium-ion batteries as major energy storage devices is of vital importance, as unexpected battery failures could result in enormous economic and societal losses. Accurate estimation of the state-of-charge (SoC) and state-of-health (SoH) for an operating battery system, as a critical task for battery health management, greatly depends on the validity and generalizability of battery models. Due to the variability and uncertainties involved in battery design, manufacturing, and operation, developing a generally applicable battery physical model is a big challenge. To eliminate the dependency of SoC and SoH estimation on battery physical models, this paper presents a generic self-cognizant dynamic system approach for lithium-ion battery health management, which integrates an artificial neural network (ANN) with a dual extended Kalman filter (DEKF) algorithm. The ANN is trained offline to model the battery terminal voltages to be used by the DEKF. With the trained ANN, the DEKF algorithm is then employed online for SoC and SoH estimation, where voltage outputs from the trained ANN model are used in DEKF state-space equations to replace the battery physical model. Experimental results are used to demonstrate the effectiveness of the developed self-cognizant dynamic system approach for battery health management.