This paper presents a general stochastic control framework for determining drug dosage regimens where the sample times, dosing times, desired goals, etc., occur at different times and in an asynchronous fashion. In the special case of multiple models with linear dynamics and quadratic cost (MMLQ), it is shown that the optimal open-loop stochastic control with linear control/state constraints can be solved exactly and efficiently as a quadratic program. This provides a simple and flexible method for computing open-loop feedback designs of drug dosage regimens. An implementation of the MMLQ adaptive control approach is demonstrated on a Lidocaine infusion process. For this example, the resulting MMLQ regimen is more effective than the MAP Bayesian regimen at reducing interpatient variability and keeping patients in the therapeutic range.