Hypnosis-Sedation Formulation for Unique Steady-State Solution in Predictive Control of Anesthesia

In anesthesia, multiple-input single-output (MISO) control structures - such as using Propofol and Remifentanil as inputs with Bispectral index (BIS) as the sole output - often lead to non-unique steady-state solutions, making it difficult to identify a physiologically interpretable drug combination. In this study, we propose an extended framework that incorporates both BIS and nociception level (NOL) indices as outputs, yielding a well-posed multiple-input multiple-output (MIMO) formulation. Based on response surface models, we derive an analytic and unique drug combination corresponding to a clinically relevant sedation and nociception level. Around the operating point, a linear model is obtained and employed as the predictive model within a model predictive control (MPC) scheme. The resulting MPC controller is implemented in both the induction and maintenance phases of anesthesia and evaluated using standard performance metrics. Simulation results over ten patient profiles confirm the controller's ability to ensure fast convergence, accurate tracking, and robustness to inter-patient variability and external disturbances.