Residual-Based Fractional-Order Model Predictive Control for Automated Co-Administration of Anesthetic Drugs

Closed-loop regulation of the bispectral index (BIS) during propofol–remifentanil co-administration is challenging because of nonlinear drug interactions, patient variability, model uncertainty, external disturbances, and infusion constraints. This paper proposes a residual-based fractional-order model predictive control (RB-FOMPC) method within the Extended Prediction Self-Adaptive Control (EPSAC) framework. FOMPC is obtained by introducing fractional-order weights into the EPSAC cost function, while an inverse Hill mapping handles the nonlinear BIS–drug relationship outside the online quadratic programming problem. RB-FOMPC further augments the FOMPC prediction with a bounded prediction of future residual variation generated by a delayed low-order residual model. During a predefined induction window, the one-sided correction is applied according to a filtered BIS-derived effect-site residual indicating nominal-model underestimation. A normalized infusion-ratio parameter coordinates the propofol and remifentanil inputs. Monte Carlo analysis showed that RB-FOMPC preserved the nominal FOMPC performance under inter-patient variability and substantially reduced excessive BIS undershoot under intra-patient model perturbations. Overall, the simulation results indicate that the residual-based predictive correction can selectively reduce induction-phase BIS undershoot under the evaluated nominal-model-underestimation conditions, while preserving the nominal performance of FOMPC.