Scenario quantile predictive control of bioreactor cultivation under kinetic parameter uncertainty

Abstract

Bioreactor feeding requires a balance between product formation, substrate limits, and uncertain kinetics. This study examines an empirical scenario-quantile model predictive controller that constrains an order statistic of predicted substrate concentrations and adds a quadratic exceedance penalty. The reported simulation campaign uses a constant-volume, three-state continuous-culture surrogate with Monod growth, product inhibition, Luedeking–Piret product formation, and six lognormally dispersed kinetic parameters. Thirty parameter draws crossed with five process-noise seeds give 150 paired runs per controller. The proposed controller has a reported final titer of 5.049 ± 1.593 g/L and a pooled step violation frequency of 4.9%, compared with 2.788 ± 1.130 g/L for Open-Loop (OL) nominal optimization, 4.798 ± 1.516 g/L for Proportional–Integral (PI) control, 4.913 ± 1.506 g/L for fixed-margin  Model Predictive Control (MPC), 5.044 ± 1.545 g/L for nominal MPC, and 5.059 ± 1.576 g/L for hard-scenario MPC. The hard-scenario controller has fewer observed violations, while an 80/90/95% order-statistic ablation changes violation frequencies from 7.9% to 2.9% with small mean-titer differences. These observations support a tunable empirical risk mechanism at the tested scale. They establish neither a finite-sample chance-constraint guarantee nor a joint batch safety guarantee. Inference, changing-volume fed-batch dynamics, and structural model error remain outside the executed comparison; the nested simulation design also limits interpretation of the reported run-level significance tests.