Intelligent agents are often faced with the need to choose actions with uncertain consequences, and to modify those actions according to ongoing sensory processing and changing task demands. The requisite ability to dynamically modify or cancel planned actions is known as inhibitory control in psychology. We formalize inhibitory control as a rational decision-making problem, and apply to it to the classical stop-signal task. Using Bayesian inference and stochastic control tools, we show that the optimal policy systematically depends on various parameters of the problem, such as the relative costs of different action choices, the noise level of sensory inputs, and the dynamics of changing environmental demands. Our normative model accounts for a range of behavioral data in humans and animals in the stop-signal task, suggesting that the brain implements statistically optimal, dynamically adaptive, and reward-sensitive decision-making in the context of inhibitory control problems.