The integration of advanced machine learning (ML) models with classical control theory, particularly Model Predictive Control (MPC), represents a significant leap forward in the optimization of complex bioprocesses. Traditional bioprocess control often relies on simplified, linear models that struggle to capture the non-linear dynamics and inherent variability of biological systems. ML-derived predictive models, however, offer a powerful solution by accurately mapping the relationship between control inputs, current process states, and predicted future outcomes.
At the core of this advanced control strategy is the predictive capability. The ML model takes the current state of the system ($\mathbf{x}(t)$), the applied control inputs ($\mathbf{u}(t)$), and predicts the system’s evolution over a defined time interval, yielding the predicted future state ($\mathbf{x}(t+\Delta t)$). This predictive power is crucial because it allows the control system to act proactively, anticipating deviations before they occur, rather than merely reacting to measured errors.
This predictive model feeds directly into the Model Predictive Control (MPC) algorithm. At each discrete time step, the MPC solves a constrained optimization problem. The objective is to find the optimal sequence of control actions ($\mathbf{u}(t), \dots, \mathbf{u}(t+H-1)$) that minimizes a defined cost function, $J(\mathbf{x}, \mathbf{u})$.
The cost function, $J$, is typically engineered to balance multiple competing objectives. For instance, in bioprocessing, $J$ might be designed to minimize the deviation of a critical quality attribute (like target titer) from its optimal setpoint, while simultaneously penalizing excessive or rapid changes in control effort (such as pump rates or temperature adjustments). This dual objective ensures that the process is driven toward the target while maintaining operational stability and minimizing resource consumption.
The optimization is performed over a defined prediction horizon, $H$. This horizon dictates how far into the future the controller plans its actions. The MPC calculates the optimal sequence of control actions ($\mathbf{u}^*$) that minimizes $J$ over this entire horizon. Crucially, this optimization is subject to two sets of constraints: first, the inherent dynamics and limitations imposed by the bioprocess model itself (e.g., maximum achievable growth rate); and second, the physical limits of the equipment (e.g., maximum pump rate, allowable temperature range). These constraints ensure that the calculated optimal actions are physically realizable and safe.
A key operational feature of MPC is its receding horizon implementation. After solving for the optimal sequence $\mathbf{u}^*$, the controller does not implement the entire sequence. Instead, it only implements the first calculated action, $\mathbf{u}(t)$. Once this action is applied and the system moves to the next time step, the entire process repeats: the system measures the new state $\mathbf{x}(t+\Delta t)$, and the MPC re-solves the optimization problem using the updated state and the remaining prediction horizon. This continuous cycle of prediction, optimization, and correction allows the system to adapt robustly to unmodeled disturbances, biological variability, and changing operating conditions, leading to superior process control and enhanced overall yield.