Objective. The goal of this research is to demonstrate proof-of-principle for managing intrafraction motion via feedback control of delivered dose to achieve dosimetry comparable to respiratory gating without compromising delivery efficiency. Approach. We develop a stochastic control approach for step-and-shoot intensity-modulated radiotherapy (IMRT) in which the cumulative delivered dose and future trajectory of intrafraction motion are dynamically estimated by combining pre-treatment four-dimensional computed tomography imaging and intrafraction respiratory-motion surrogates. The IMRT plan is then re-optimized in real time to ensure delivery of the planned dose in the presence of free-breathing motion. We compare the performance of the proposed approach against traditional motion-management techniques, namely, respiratory gating and internal target volume (ITV) planning, using the four-dimensional extended cardiac-torso computational phantom. Main results. We simulate the delivery of treatment plans for a lung tumor in the presence of variable breathing amplitude, tumor size, and location. Results show that the proposed method reduces irradiated tissue volume compared to ITV treatment. Additionally, it significantly reduces treatment time compared to traditional respiratory-gated treatment, without compromising the dosimetric quality. Significance. Respiratory gating is a common technique to manage intrafraction motion. While gating supports reduced treatment volumes, it also prolongs the treatment delivery time. The proposed stochastic control approach can help improve the delivery efficiency of respiratory gating without compromising the dose quality.