Water Resources Management

, Volume 33, Issue 2, pp 677–696 | Cite as

Scenario-Based Hierarchical and Distributed MPC for Water Resources Management with Dynamical Uncertainty

  • P. VelardeEmail author
  • X. Tian
  • A. D. Sadowska
  • J. M. Maestre


A real-time control scheme informed by a streamflow forecast is presented for the optimal operation of water resources systems composed of multiple and spatially distributed systems, affected by hydroclimatic disturbances. The approach uses a two-layer scenario-based hierarchical and distributed model predictive controller (HD-MPC) to deal with the operational water management problem under dynamical uncertainty. The higher layer collects and coordinates forecast information, which is rendered into possible realizations of the uncertainties and sent to the local agents. The lower layer solves a distributed optimization problem related to the actual management objectives. The HD-MPC method is demonstrated through a simulation of the North Sea Canal system as a real-world case study. The results show the benefits of the proposed compared to over other types of MPC controllers.


Water resource management Model predictive control Distributed control Dynamical uncertainty Hierarchical control 



Financial support was provided by the Spanish Ministry of Economy and Competitiveness under grant DPI2017-86918-R.

Compliance with Ethical Standards

Conflict of interests

The authors declare that they have no conflict of interest.


  1. Beh EHY, Maier HR, Dandy GC (2015) Adaptive, multiobjective optimal sequencing approach for urban water supply augmentation under deep uncertainty. Water Resour Res 51(3):1529–1551CrossRefGoogle Scholar
  2. Biegel B, Stoustrup J, Andersen P (2014) Distributed MPC via dual decomposition Distributed model predictive control made easy. Springer, pp 179–192Google Scholar
  3. Characklis GW, Kirsch BR, Ramsey J, Dillard KE, Kelley CT (2006) Developing portfolios of water supply transfers. Water Resour Res 42(5):1–14CrossRefGoogle Scholar
  4. Clemmens AJ, Schuurmans J (2004) Simple Optimal Downstream Feedback Canal Controllers: Theory. J Irrig Drain Eng 130(1):26–34CrossRefGoogle Scholar
  5. Delgoda DK, Saleem SK, Halgamuge MN, Malano H (2013) Multiple model predictive flood control in regulated river systems with uncertain inflows. Water Resour Manag 27(3):765–790CrossRefGoogle Scholar
  6. Di Cairano S, Bernardini D, Bemporad A, Kolmanovsky IV (2014) Stochastic MPC with learning for driver-predictive vehicle control and its application to HEV energy management. IEEE Trans Control Syst Technol 22(3):1018–1031CrossRefGoogle Scholar
  7. Grosso JM, Velarde P, Ocampo-Martinez C, Maestre JM, Puig V (2017) Stochastic model predictive control approaches applied to drinking water networks. Optimal Control Appl Methods 38(4):541–558CrossRefGoogle Scholar
  8. Growe-Kuska N, Heitsch H, Romisch W (2003) Scenario reduction and scenario tree construction for power management problems. In: Proceedings of 2003 IEEE Bologna Power Tech Conference, vol. 3, pp 7, vol 3–Google Scholar
  9. Haasnoot M, Kwakkel JH, Walker W (2013) Dynamic adaptive policy pathways: A method for crafting robust decisions for a deeply uncertain world. Glob Environ Chang 23(2):485–498CrossRefGoogle Scholar
  10. Jurado I, Maestre JM, Velarde P, Ocampo-Martinez C, Fernandez I, Tejera BI, del Prado JR (2016) Stock management in hospital pharmacy using chance-constrained model predictive control. Comput Biol Med 72:248–255CrossRefGoogle Scholar
  11. Kwakkel JH, Walker WE, Haasnoot M (2016) Coping with the Wickedness of Public Policy Problems: Approaches for Decision Making under Deep Uncertainty. Journal of Water Resources Planning and Management p 01816001Google Scholar
  12. Loucks DP, van Beek E, Stedinger JR, Dijkman JP, Villars MT (2005) Water resources systems planning and management and applications: An Introduction to Methods, Models and Applications, vol. 51, 1 edn Springer International PublishingGoogle Scholar
  13. Maciejowski J (2002) Predictive control with constraints. Prentice Hall, EssexGoogle Scholar
  14. Maestre JM, Negenborn RR (2014) Distributed model predictive control made easy. Springer, BerlinCrossRefGoogle Scholar
  15. Maestre JM, Raso L, van Overloop PJ, De Schutter B (2013a) Distributed tree-based model predictive control on a drainage water system. J Hydroinf 15(2):335CrossRefGoogle Scholar
  16. Maestre JM, Raso L, Overloop PJV, De Schutter B (2013b) Distributed tree-based model predictive control on a drainage water system. J Hydroinf 15(2):335–347CrossRefGoogle Scholar
  17. Maier H, Guillaume J, van Delden H, Riddell G, Haasnoot M, Kwakkel J (2016) An uncertain future, deep uncertainty, scenarios, robustness and adaptation: How do they fit together?. Environ Model Softw 81:154–164CrossRefGoogle Scholar
  18. Malaterre PO, Rogers DC, Schuurmans J (1998) Classification of canal control algorithms controlled variables. J Irrig Drain Eng 124(1):1–18CrossRefGoogle Scholar
  19. Matrosov ES, Huskova I, Kasprzyk JR, Harou JJ, Reed P (2015) Many-objective optimization and visual analytics reveal key planning trade-offs for London’s water supply. J Hydrol 531(2005):1040–1053CrossRefGoogle Scholar
  20. Ocampo-Martinez C, Puig V, Cembrano G, Quevedo J (2013) Application of predictive control strategies to the management of complex networks in the urban water cycle. IEEE Control Syst Mag 33(1):15–41CrossRefGoogle Scholar
  21. Raso L, Giesen N, Stive P, Schwanenberg D, van Overloop PJ (2013) Tree structure generation from ensemble forecasts for real time control. Hydrol Process 27(1):75–82CrossRefGoogle Scholar
  22. Raso L, Schwanenberg D, van de Giesen NC, van Overloop PJ (2014) Short-term optimal operation of water systems using ensemble forecasts. Adv Water Resour 71:200–208CrossRefGoogle Scholar
  23. Reed P, Hadka D, Herman J, Kasprzyk J, Kollat J (2013) Evolutionary multiobjective optimization in water resources: The past, present, and future. Adv Water Resour 51:438–456CrossRefGoogle Scholar
  24. Richalet J, Rault A, Testud J, Papon J (1978) Model predictive heuristic control: Applications to industrial processes. Automatica 14(5):413–428CrossRefGoogle Scholar
  25. 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):3009–3018CrossRefGoogle Scholar
  26. Schuurmans J (1997) Control of water levels in open channels. Delft university of Technology, Ph.D. thesisGoogle Scholar
  27. Stelling GS, Duinmeijer SPA (2003) A staggered conservative scheme for every froude number in rapidly varied shallow water flows. Int J Numer Methods Fluids 43 (12):1329–1354CrossRefGoogle Scholar
  28. Šutienė K, Makackas D, Pranevičius H (2010) Multistage k-means clustering for scenario tree construction. Informatica 21(1):123–138Google Scholar
  29. Tian X, Negenborn RR, van Overloop PJ, Mari̇a Maestre J, Sadowska A, van de Giesen N (2017) Efficient multi-scenario model predictive control for water resources management with ensemble streamflow forecasts. Adv Water Resour 109:58–68CrossRefGoogle Scholar
  30. van Overloop PJ (2006) Model predictive control on open water systems. Delft University of Technology, Ph.D. thesisGoogle Scholar
  31. van Overloop PJ, Weijs S, Dijkstra S (2008) Multiple model predictive control on a drainage canal system. Control Eng Pract 16(5):531–540CrossRefGoogle Scholar
  32. van Overloop PJ, Negenborn RR, De Schutter B, van De Giesen NC (2010) Predictive control for national water flow optimization in The Netherlands. Intelligent Infrastructures 42:439–461CrossRefGoogle Scholar
  33. Vogel RM, Lall U, Cai X, Rajagopalan B, Weiskel PK, Hooper RP, Matalas NC (2015) Hydrology: The interdisciplinary science of water. Water Resour Res 51(6):4409–4430CrossRefGoogle Scholar
  34. Walker W, Haasnoot M, Kwakkel J (2013) Adapt or perish: A review of planning approaches for adaptation under deep uncertainty. Sustainability 5(3):955–979CrossRefGoogle Scholar
  35. Xu M (2013) Real-time control of combined water quantity & quality in open channels. Delft University of Technology, TU DelftGoogle Scholar
  36. Zafra-Cabeza A, Maestre JM, Ridao MA, Camacho EF, Sánchez L (2011) A hierarchical distributed model predictive control approach to irrigation canals: A risk mitigation perspective. J Process Control 21(5):787–799CrossRefGoogle Scholar
  37. Zeff HB, Herman JD, Reed PM, Characklis GW (2016) Cooperative drought adaptation: Integrating infrastructure development, conservation, and water transfers into adaptive policy pathways. Water Resour Res 52(9):7327–7346CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Facultad de Ciencias de la Ingeniería e IndustriasUniversidad UTEQuitoEcuador
  2. 2.System Engineering and Automation Department, School of EngineeringUniversity of SevilleSevilleSpain
  3. 3.Department of Water ManagementDelft University of TechnologyDelftThe Netherlands
  4. 4.College of HydrometeorologyNanjing University of Information Science & TechnologyNanjingChina
  5. 5.Schlumberger Cambridge ResearchCambridgeUK

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