Real-time Projected Gradient-based Nonlinear Model Predictive Control with an Application to Anesthesia Control

TL;DR

This paper introduces a real-time projected gradient-based NMPC method for nonlinear control problems, demonstrating its effectiveness in anesthesia drug infusion by handling uncertainties and ensuring safety.

Contribution

It proposes a novel real-time NMPC scheme using projected gradient descent, enabling faster feedback and stability guarantees for complex nonlinear control tasks.

Findings

Successfully regulates anesthesia hypnosis under disturbances

Achieves benchmark control performance

Handles model uncertainties effectively

Abstract

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.