Management of weighted scenarios in stochastic environments using model predictive control
DOI:
https://doi.org/10.17979/ja-cea.2025.46.12266Keywords:
Predictive control, Stochastic system, Weighted scenarios, Probabilistic and robust control, Optimal controlAbstract
This paper presents a detailed formulation of scenario-weighted model predictive control (WS-MPC) tailored for linear systems under uncertainty. The proposed approach combines robust optimization techniques with generating multiple dynamic scenarios of the system and assigning differentiated weights to the worst-case scenario within the control problem. This strategy enhances the system’s resilience to stochastic disturbances and modeling uncertainties, improving the controller’s ability to anticipate unexpected behaviors. Furthermore, WS-MPC dynamically adjusts control actions based on the evolution of all considered scenarios, while ensuring system feasibility and stability under unfavorable conditions. Simulation results demonstrate that the proposed method increases the operational robustness of the system and provides a safer and more reliable response to unexpected variations. In particular, this controller has been implemented in an academic case study focused on store inventory management.
References
Arcari, E., Iannelli, A., Carron, A., Zeilinger, M. N., 2023. Stochastic MPC with robustness to bounded parameteric uncertainty. IEEE Transactions on Automatic Control 68 (12), 7601–7615. DOI: 10.1109/TAC.2023.3294868
Bemporad, A., Borrelli, F., Morari, M., Sept 2003. Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control 48 (9), 1600–1606. DOI: 10.1109/TAC.2003.816984
Ben-Tal, A., Ghaoui, L., Nemirovski, A., 2009. Robust Optimization. Princeton University Press. DOI: 10.1515/9781400831050
Bertsimas, D., Brown, D. B., Caramanis, C., 2011. Theory and applications of robust optimization. SIAM review 53 (3), 464–501. DOI: 10.48550/arXiv.1010.5445
Birge, J. R., Louveaux, F., 2011. Introduction to stochastic programming. Springer Science & Business Media. DOI: 10.1007/978-1-4614-0237-4
Calafiore, G. C., Fagiano, L., 2012. Robust model predictive control via scenario optimization. IEEE Transactions on Automatic Control 58 (1), 219– 224. DOI: 10.1109/TAC.2012.2203054
Hernández-Rivera, Andrés et al. / Jornadas de Automática, 46 (2025) Camacho, E. F., Berenguel, M., Rubio, F. R., Mart´ınez, D., 2012. Control of solar energy systems. Springer, London, England. DOI: 10.1007/978-0-85729-916-1
Camacho, E. F., Bordons, C., Maestre, J. M., 2025. Model Predictive Control. Third Edition. Springer-Verlag, London, England.
Coppens, P., Patrinos, P., 2021. Data-driven distributionally robust MPC for constrained stochastic systems. IEEE Control Systems Letters 6, 1274–1279. DOI: 10.1109/LCSYS.2021.3091628
Giulioni, L., 2015. Stochastic model predictive control with application to distributed control systems. Ph.D. thesis, Politecnico di Milano.
Grosso, J., Ocampo-Martinez, C., Puig, V., Joseph, B., 2014. Chanceconstrained model predictive control for drinking water networks. Journal of Process Control 24 (5), 504–516. DOI: 10.1016/j.jprocont.2014.01.010
Maciejowski, J., 2002. Predictive control with constraints. Prentice Hall, Essex, England.
Mark, C., Liu, S., 2020. Stochastic MPC with distributionally robust chance constraints. IFAC-PapersOnLine 53 (2), 7136–7141. DOI: 10.1016/j.ifacol.2020.12.521
Schildbach, G., Fagiano, L., Frei, C., Morari, M., 2014. The scenario approach for stochastic model predictive control with bounds on closed-loop constraint violations. Automatica 50 (12), 3009–3018. DOI: 10.1016/j.automatica.2014.10.035
Shapiro, A., Dentcheva, D., Ruszczynski, A., 2021. Lectures on stochastic programming: modeling and theory. SIAM. DOI: 10.1137/1.9781611976595
Tian, X., Negenborn, R. R., van Overloop, P.-J., Maestre, J. M., Sadowska, A., van de Giesen, N., 2017. Efficient multi-scenario model predictive control for water resources management with ensemble streamflow forecasts. Advances in water resources 109, 58–68. DOI: 10.1016/j.advwatres.2017.08.015
van Ackooij, W., Henrion, R., P´erez-Aros, P., 2020. Generalized gradients for probabilistic/robust (probust) constraints. Optimization 69 (7-8), 1451–1479. DOI: 10.1080/02331934.2019.1576670
van Overloop, P.-J., Weijs, S., Dijkstra, S., 2008. Multiple model predictive control on a drainage canal system. Control Engineering Practice 16 (5), 531–540. DOI: 10.1016/j.conengprac.2007.06.002
Velarde, P., Valverde, L., Maestre, J., Ocampo-Martinez, C., Bordons, C., 2017. On the comparison of stochastic model predictive control strategies applied to a hydrogen-based microgrid. Journal of Power Sources 343, 161–173. DOI: 10.1016/j.jpowsour.2017.01.015
Velarde, P., Zafra-Cabeza, A., Márquez, J. J., Maestre, J. M., Bordons, C., 2023. Stochastic MPC-based reconfiguration approaches for microgrids. IEEE Transactions on Control Systems Technology. DOI: 10.1109/TCST.2023.3342135
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Copyright (c) 2025 Andrés Hernández-Rivera, Pablo Velarde, Ascensión Zafra-Cabeza, Francisco Javier Muros, José M. Maestre
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