Sequences of different drugs have shown potential to improve treatment strategies for cancer. Typical switched system approaches model the population dynamics of each drug independently, not rigorously considering the effects of pretreatment or drug-drug interactions. In this paper, a general model family incorporating pre-treatment effects and biological domain knowledge is proposed, and a model from this family is identified by using a novel experimental data set of two-drug sequences. Leveraging the data, a simulator for the cell population dynamics under sequences of up to nine drugs is developed and used to empirically evaluate the performance of a set of closed-loop drug scheduling controllers. We used the controllers to identifying promising drug schedules in silico and evaluated them in vitro. The experiments validated the effectiveness of the identified schedules in reducing the number of living cells to less than 10% of the initial. While only treating with certain toxic drugs achieves similar effectiveness, the schedules use toxic drugs for significantly shorter times which likely reduces toxicity to non-cancer cells.