Gain-Scheduled Optogenetic Feedback for Disturbance Rejection in Bacterial Batch Cultures

Precise regulation of gene expression in batch bacterial cultures is challenging because the underlying dynamics vary with cellular physiological state over time. Although cell-silicon systems enable rapid, real-time optogenetic control, disturbance rejection remains difficult in batch culture because the plant dynamics shift across growth phases, limiting the effectiveness of fixed-gain controllers designed under constant-growth assumptions. Here, we present a multiscale model-guided feedback control framework for disturbance rejection in batch E. coli cultures. Frequency-response analysis shows that the input-output dynamics of gene expression depend strongly on growth phase, revealing operating-point-dependent limits on the disturbance rejection performance of a fixed-gain PID controller. To address this limitation, we develop two growth-aware control strategies: a gain-scheduled PID (PID-GS) controller that adapts to cellular physiological state, and a gain-scheduled feedback-feedforward controller (PID-GS-FF) that further compensates for growth perturbations. We also introduce a controller evaluation framework that identifies three distinct operating regimes for targeted experimental validation. Together, these results show that accounting for growth-state-dependent dynamics is necessary for robust disturbance rejection in batch culture and provide a control-oriented framework for regulating living systems with shifting operating conditions.