Stochastic model predictive control approaches applied to drinking water networks

Summary Control of drinking water networks is an arduous task, given their size and the presence of uncertainty in water demand. It is necessary to impose different constraints for ensuring a reliable water supply in the most economic and safe ways. To cope with uncertainty in system disturbances due to the stochastic water demand/consumption and optimize operational costs, this paper proposes three stochastic model predictive control (MPC) approaches, namely, chance-constrained MPC, tree-based MPC, and multiple-scenario MPC. A comparative assessment of these approaches is performed when they are applied to real case studies, specifically, a sector and an aggregate version of the Barcelona drinking water network in Spain. Copyright © 2016 John Wiley & Sons, Ltd.

[1]  Pu Li,et al.  Advances and applications of chance-constrained approaches to systems optimisation under uncertainty , 2013, Int. J. Syst. Sci..

[2]  S. Engell,et al.  A new Robust NMPC Scheme and its Application to a Semi-batch Reactor Example* , 2012 .

[3]  Alexander Shapiro,et al.  Convex Approximations of Chance Constrained Programs , 2006, SIAM J. Optim..

[4]  Peter-Jules van Overloop,et al.  Multiple Model Predictive Control on a drainage canal system , 2008 .

[5]  Carlos Ocampo-Martinez,et al.  An application of chance-constrained model predictive control to inventory management in Hospitalary Pharmacy , 2014, 53rd IEEE Conference on Decision and Control.

[6]  Holger R. Maier,et al.  Optimal sequencing of water supply options at the regional scale incorporating alternative water supply sources and multiple objectives , 2014, Environ. Model. Softw..

[7]  Michael Nikolaou,et al.  Chance‐constrained model predictive control , 1999 .

[8]  Kristina Sutiene,et al.  Multistage K-Means Clustering for Scenario Tree Construction , 2010, Informatica.

[9]  Dirk Schwanenberg,et al.  Short-term optimal operation of water systems using ensemble forecasts , 2014 .

[10]  C. J. Brouckaert,et al.  Optimal operation of water distribution networks by predictive control using MINLP , 2004 .

[11]  Lorenzo Fagiano,et al.  Randomized Solutions to Convex Programs with Multiple Chance Constraints , 2012, SIAM J. Optim..

[12]  Jan M. Maciejowski,et al.  Predictive control : with constraints , 2002 .

[13]  H. van de Water,et al.  The certainty equivalence property in stochastic control theory , 1981 .

[14]  Werner Römisch,et al.  Scenario tree modeling for multistage stochastic programs , 2009, Math. Program..

[15]  Basil Kouvaritakis,et al.  MPC for Stochastic Systems , 2007 .

[16]  Enrique Cabrera,et al.  Performance Indicators for Water Supply Services: Third Edition , 2006 .

[17]  Thomas D. Sandry,et al.  Probabilistic and Randomized Methods for Design Under Uncertainty , 2007, Technometrics.

[18]  Peter-Jules van Overloop,et al.  Tree-Scenario Based Model Predictive Control , 2010 .

[19]  Vicenç Puig,et al.  A service reliability model predictive control with dynamic safety stocks and actuators health monitoring for drinking water networks , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[20]  C. Ocampo‐Martinez,et al.  Application of predictive control strategies to the management of complex networks in the urban water cycle [Applications of Control] , 2013, IEEE Control Systems.

[21]  András Prékopa Static Stochastic Programming Models , 1995 .

[22]  Carlos Ocampo-Martinez,et al.  Stock management in hospital pharmacy using chance-constrained model predictive control , 2016, Comput. Biol. Medicine.

[23]  B. De Schutter,et al.  Distributed tree-based model predictive control on a drainage water system , 2013 .

[24]  Sebastian Engell,et al.  Non-conservative robust Nonlinear Model Predictive Control via scenario decomposition , 2013, 2013 IEEE International Conference on Control Applications (CCA).

[25]  Laureano F. Escudero,et al.  WARSYP: a robust modeling approach for water resources system planning under uncertainty , 2000, Annals of Operations Research.

[26]  Alberto Bemporad,et al.  Scenario-based model predictive control of stochastic constrained linear systems , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[27]  Vicenç Puig,et al.  On the assessment of tree-based and chance-constrained predictive control approaches applied to drinking water networks , 2014 .

[28]  S Leirens,et al.  Coordination in urban water supply networks using distributed model predictive control , 2010, Proceedings of the 2010 American Control Conference.

[29]  T. Alamo,et al.  Stochastic Programming Applied to Model Predictive Control , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[30]  P. J. Van Overloop,et al.  Model Predictive Control on Open Water Systems , 2006 .

[31]  Lorenzo Fagiano,et al.  The scenario approach for Stochastic Model Predictive Control with bounds on closed-loop constraint violations , 2013, Autom..

[32]  R. Tyrrell Rockafellar,et al.  Scenarios and Policy Aggregation in Optimization Under Uncertainty , 1991, Math. Oper. Res..

[33]  N. Growe-Kuska,et al.  Scenario reduction and scenario tree construction for power management problems , 2003, 2003 IEEE Bologna Power Tech Conference Proceedings,.

[34]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[35]  Masahiro Ono,et al.  Iterative Risk Allocation: A new approach to robust Model Predictive Control with a joint chance constraint , 2008, 2008 47th IEEE Conference on Decision and Control.

[36]  Peter Kall,et al.  Stochastic Linear Programming , 1975 .

[37]  Eduardo Bautista,et al.  Real-time implementation of model predictive control on Maricopa-Stanfield Irrigation and Drainage District's WM Canal. , 2010 .

[38]  J. M. Grosso,et al.  Chance-Constrained Model Predictive Control for Drinking Water Networks , 2014 .

[39]  Giuseppe Carlo Calafiore,et al.  Research on probabilistic methods for control system design , 2011, Autom..

[40]  Eduardo F. Camacho,et al.  Model predictive control in the process industry , 1995 .

[41]  Dirk Schwanenberg,et al.  Tree structure generation from ensemble forecasts for real time control , 2013 .

[42]  T. B. M. J. Ouarda,et al.  Chance-constrained optimal control for multireservoir system optimization and risk analysis , 2001 .

[43]  Warren E. Walker,et al.  Adapt or Perish: A Review of Planning Approaches for Adaptation under Deep Uncertainty , 2013 .

[44]  Eduardo F. Camacho,et al.  A hierarchical distributed model predictive control approach to irrigation canals: A risk mitigation perspective , 2011 .

[45]  Bart De Schutter,et al.  Distributed tree-based model predictive control on an open water system , 2012, 2012 American Control Conference (ACC).

[46]  A. Charnes,et al.  Deterministic Equivalents for Optimizing and Satisficing under Chance Constraints , 1963 .