Proceedings of ESCAPE 36ISSN: 2818-4734
Volume: 5 (2026)
Table of Contents
LAPSE:2026.0527
Published Article
LAPSE:2026.0527
Identification and Self-optimization of Robust Nominal Operating Ranges Using Proximal Policy Optimization
Ashish Yewale, Brahim Benyahia
June 12, 2026
Abstract
Reliable process operation under uncertainty remains a fundamental challenge in chemical and pharmaceutical manufacturing. Variability arising from feed fluctuations, material properties, external disturbances, and uncertain model parameters can significantly impact feasibility and performance when operating ranges are designed under nominal assumptions. Design Space Identification (DSI) addresses these limitations by defining a Probabilistic Design Space (PDS), within which process constraints are satisfied with a prescribed confidence level. However, identifying and extracting robust and practically usable nominal operating ranges (NORs) from complex, high-dimensional, and nonconvex PDSs remains computationally demanding. This work proposes a novel reinforcement learning (RL)-based framework for automated identification of the largest robust hyper-rectangular NOR fully contained within a given PDS. The design centering problem is formulated as a sequential decision-making task and solved using the Proximal Policy Optimization (PPO) algorithm. By interacting with a probabilistic feasibility environment, the RL agent adaptively adjusts the location and size of the NOR to maximize its area while enforcing probabilistic constraint satisfaction. Deep neural network policies enable efficient exploration of nonlinear feasibility boundaries without exhaustive sampling or gradient-based optimization. The approach is demonstrated on a tablet lubrication case study with parametric uncertainty. Results show rapid convergence to well-located, near-maximal NORs using substantially fewer probabilistic feasibility evaluations than conventional grid-based or Monte Carlo methods. The proposed PPO-based framework provides a scalable and data-efficient solution for robust operating range identification in uncertainty-aware process design.
Keywords
Nominal Operating Range NOR, Operational flexibility, Probabilistic design space PDS, Proximal Policy Optimization, Reinforcement Learning
Suggested Citation
Yewale A, Benyahia B. Identification and Self-optimization of Robust Nominal Operating Ranges Using Proximal Policy Optimization. Systems and Control Transactions 5:2587-2593 (2026) https://doi.org/10.69997/sct.189137
Author Affiliations
Yewale A: Department of Chemical Engineering, Loughborough University, Leicestershire, LE11 3TU, UK
Benyahia B: Department of Chemical Engineering, Loughborough University, Leicestershire, LE11 3TU, UK
[Login] to see author email addresses.
Journal Name
Systems and Control Transactions
Volume
5
First Page
2587
Last Page
2593
Year
2026
Publication Date
2026-06-12
Version Comments
Original Submission
Other Meta
PII: 2587-2593-648-SCT-5-2026, Publication Type: Journal Article
Record Map
Published Article

LAPSE:2026.0527
This Record
External Link

https://doi.org/10.69997/sct.189137
Publisher Version
Download
Files
Jun 12, 2026
Main Article
License
CC BY-SA 4.0
Meta
Record Statistics
Record Views
264
Version History
[v1] (Original Submission)
Jun 12, 2026
 
Verified by curator on
Jun 12, 2026
This Version Number
v1
Citations
Most Recent
This Version
URL Here
https://psecommunity.org/LAPSE:2026.0527
 
Record Owner
PSE Press
Links to Related Works
Directly Related to This Work
Publisher Version
References Cited
  1. Gao S, Benyahia B. Robust techno-economic analysis, life cycle assessment, and quality and sustainability by digital design of three alternative continuous pharmaceutical tablet manufacturing processes. Systems and Control Transactions 4:2568-2573 (2025) https://doi.org/10.69997/sct.104102
  2. Campbell, T. J. S.; Rielly, C. D.; Benyahia, B. Digital Design and Optimization of an Integrated Reaction-Extraction-Crystallization-Filtration Continuous Pharmaceutical Process. Comput. -Aided Chem. Eng. 2022, 51, 775-780 https://doi.org/10.1016/B978-0-323-95879-0.50130-2
  3. Peterson JJ, Yahyah M. A bayesian design space approach to robustness and system suitability for pharmaceutical assays and other processes. Statistics in Biopharmaceutical Research 1:441-449 (2009) https://doi.org/10.1198/sbr.2009.0037
  4. Peterson JJ. A bayesian approach to the ICH Q8 definition of design space. Journal of Biopharmaceutical Statistics 18:959-975 (2008) https://doi.org/10.1080/10543400802278197
  5. von Stosch M, Schenkendorf R, Geldhof G, Varsakelis C, Mariti M, Dessoy S, Vandercammen A, Pysik A, Sanders M. Working within the design space: do our static process characterization methods suffice?. Pharmaceutics 12:562 (2020) https://doi.org/10.3390/pharmaceutics12060562
  6. Duarte JG, Duarte MG, Piedade AP, Mascarenhas-Melo F. Rethinking pharmaceutical industry with quality by design: application in research, development, manufacturing, and quality assurance. AAPS J 27: (2025) https://doi.org/10.1208/s12248-025-01079-w
  7. Laky D, Xu S, Rodriguez JS, Vaidyaraman S, García Muñoz S, Laird C. An optimization-based framework to define the probabilistic design space of pharmaceutical processes with model uncertainty. Processes 7:96 (2019) https://doi.org/10.3390/pr7020096
  8. Meng Q, Bogle D, Charitopoulos VM. Probabilistic design space exploration and optimization via bayesian approach for a fluid bed drying process. European Journal of Pharmaceutical Sciences 210:107116 (2025) https://doi.org/10.1016/j.ejps.2025.107116
  9. Yewale A, Yuan X, Benyahia B. Robust pharmaceutical tableting process through combined probabilistic design space and flexibility analysis. Systems and Control Transactions 4:637-643 (2025) https://doi.org/10.69997/sct.128065
  10. Chiplunkar R, Pauzi SM, Sachio S, Papathanasiou MM, Kontoravdi C. Probabilistic design space identification for upstream bioprocesses under limited data availability?. Systems and Control Transactions 4:2561-2567 (2025) https://doi.org/10.69997/sct.166359
  11. Kusumo KP, Morrissey J, Mitchell H, Shah N, Chachuat B. A design centering methodology for probabilistic design space. IFAC-PapersOnLine 54:79-84 (2021) https://doi.org/10.1016/j.ifacol.2021.08.222
  12. Moshiritabrizi I, McMullen JP, Wyvratt BM, McAuley KB. A comparative study of strategies for incorporating uncertainty in design space determination for pharmaceutical manufacturing. Ind. Eng. Chem. Res. 64:21658-21668 (2025) https://doi.org/10.1021/acs.iecr.5c03037
  13. Yewale A, Yang Y, Nazemifard N, Papageorgiou CD, Rielly CD, Benyahia B. Deep reinforcement learning-based self-optimization of flow chemistry. ACS Eng. Au 5:247-266 (2025) https://doi.org/10.1021/acsengineeringau.5c00004
  14. Anandan, P.D.; Rielly, C. D.; Benyahia, B.; Optimal Control Policies of a Crystallization Process Using Inverse Reinforcement Learning, Computer Aided Chemical Engineering, 2021 51, 1093-1098 https://doi.org/10.1016/B978-0-323-95879-0.50183-1
  15. Anandan, P.D.; Rielly, C. D.; Benyahia, B.; Control of Batch and Continuous Crystallization Processes using Reinforcement Learning. Computer Aided Chemical Engineering, 2021, 50, 1371-1376 https://doi.org/10.1016/B978-0-323-88506-5.50211-4
  16. Kushner J IV, Moore F. Scale-up model describing the impact of lubrication on tablet tensile strength. International Journal of Pharmaceutics 399:19-30 (2010) https://doi.org/10.1016/j.ijpharm.2010.07.033
  17. Nassar J, Williams B, Davies C, Lief K, Elkes R. Lubrication empirical model to predict tensile strength of directly compressed powder blends. International Journal of Pharmaceutics 592:119980 (2021) https://doi.org/10.1016/j.ijpharm.2020.119980
(0.1 seconds)

[0.1 s]