Abstract: A method of rapidly charging a battery includes: (a) applying a charge to the battery using a charging profile; (b) monitoring a terminal voltage of the battery; (c) using a mathematical model to estimate a desired temporal state of charge of the battery and to estimate a predicted terminal voltage; (d) using the monitored terminal voltage of the battery and the predicted terminal voltage to determine an error; (e) applying the error to calculate a calculated state of charge of the battery; and (f) controlling the charge applied by the charging profile to urge the calculated state of charge of the battery toward the desired temporal state of charge of the battery. For use with lithium ion batteries, such feedback is used to limit ion concentration levels. Preferably, a Reduced Order Model is used to minimize computational requirements and facilitate real-time calculations.