  Medical drug infusion problems pose a combination of challenges such as
nonlinearities from physiological models, model uncertainty due to inter- and
intra-patient variability, as well as strict safety specifications. With these
challenges in mind, we propose a novel real-time Nonlinear Model Predictive
Control (NMPC) scheme based on projected gradient descent iterations. At each
iteration, a small number of steps along the gradient of the NMPC cost is
taken, generating a suboptimal input which asymptotically converges to the
optimal input. We retrieve classical Lyapunov stability guarantees by
performing a sufficient number of gradient iterations until fulfilling a
stopping criteria. Such a real-time control approach allows for higher sampling
rates and faster feedback from the system which is advantageous for the class
of highly variable and uncertain drug infusion problems. To demonstrate the
controller's potential, we apply it to hypnosis control in anesthesia of two
interacting drugs. The controller successfully regulates hypnosis even under
disturbances and uncertainty and fulfils benchmark performance criteria.
