# Dynamic Real-time Optimization of Batch Processes using Pontryagin's Minimum Principle and Set-membership Adaptation

## TL;DR

This paper introduces a real-time optimization method for batch processes that combines Pontryagin's Minimum Principle with set-membership adaptation to handle model mismatch efficiently.

## Contribution

It proposes a novel approach that reduces computational load by integrating reachable sets and online parameter estimation in a predictive control framework.

## Key findings

- Effective handling of model uncertainty using reachable sets.
- Reduced computational burden compared to traditional re-optimization.
- Successful application to batch membrane separation processes.

## Abstract

This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with frequent re-optimization. The main problem addressed in this study is the high computational burden that is usually required by such schemes. We propose an approach that uses parameterized conditions of optimality in the adaptive predictive-control fashion. The uncertainty in the model predictions is treated explicitly using reachable sets that are projected into the optimality conditions. Adaptation of model parameters is performed online using set-membership estimation. A class of batch membrane separation processes is in the scope of the presented applications, where the benefits of the presented approach are outlined.