# Stochastic MPC Design for a Two-Component Granulation Process

## TL;DR

This paper develops a stochastic model predictive control approach for a pharmaceutical granulation process, using model reduction and polynomial chaos to efficiently manage particle distribution variance in real time.

## Contribution

It introduces a novel SMPC framework combining model reduction and polynomial chaos expansion for efficient control of stochastic particulate systems.

## Key findings

- Reduced-order model effectively captures process dynamics.
- Polynomial chaos enables deterministic approximation of stochastic optimization.
- Proposed method facilitates real-time control in pharmaceutical manufacturing.

## Abstract

We address the issue of control of a stochastic two-component granulation process in pharmaceutical applications through using Stochastic Model Predictive Control (SMPC) and model reduction to obtain the desired particle distribution. We first use the method of moments to reduce the governing integro-differential equation down to a nonlinear ordinary differential equation (ODE). This reduced-order model is employed in the SMPC formulation. The probabilistic constraints in this formulation keep the variance of particles' drug concentration in an admissible range. To solve the resulting stochastic optimization problem, we first employ polynomial chaos expansion to obtain the Probability Distribution Function (PDF) of the future state variables using the uncertain variables' distributions. As a result, the original stochastic optimization problem for a particulate system is converted to a deterministic dynamic optimization. This approximation lessens the computation burden of the controller and makes its real time application possible.