In applications where it is crucial that a battery is recharged from the partially discharged state in the minimum time, it is crucial to honor the technological constraints related to maximum safe battery terminal voltage and maximum continuous charging current prescribed by the battery cell manufacturer. To this end, this contribution outlines the design and comprehensive simulation analysis of an adaptive battery charging system relying on battery open-circuit voltage estimation in real time. A pseudo-random binary sequence test signal and model reference adaptive system are used for the estimation of lithium titanate battery cell electrical circuit model parameters, with the design methodology based on the Lyapunov stability criterion. The proposed adaptive charger is assessed against the conventional constant-current/constant-voltage charging system. The effectiveness of the real-time parameter estimator, along with both the adaptive and traditional charging systems for the lithium titanate battery cell, is validated through simulations and experiments on a dedicated battery test bench.