The observed shift to a fully electrified transport sector with steadily increasing sales of battery electric vehicles has led to their wider use under demanding operation conditions, e.g., more frequent fast charging due to a higher degree of utilization with an increased share of operation under low ambient temperatures. These critical edge cases have to be precisely controlled by the battery management system to avoid accelerated battery aging and, in the worst case, safety-critical battery failure events. In this article, we present a model-based, health-aware fast charging strategy for current control of lithium-ion batteries to prevent the onset of non-linear aging and to prolong the cycle life. An electrochemical model of reduced order is used to avoid non-linear aging due to lithium plating. The model is regularly updated alongside the state-of-health of the battery to account for the rise of resistance. Extensive cycle life results reveal that the charging time can be significantly reduced while the cycle life can be prolonged compared to conventional charging. As the strategy is based on an electrochemical model of reduced order, inheriting the physics of lithium-ion batteries, the results can be easily transferred to other cell chemistries and/or formats.