Abstract
Two formulations of the stochastic model predictive control (SMPC) problem for the control of large-scale drinking-water networks are presented in this chapter. The first approach, named chance-constrained MPC, makes use of the assumption that the uncertain future water demands follow some known continuous probability distribution while at the same time, certain risk (probability) for the state constraints to be violated is allocated. The second approach, named tree-based MPC, does not require any assumptions on the probability distribution of the demand estimates, but brings about a complexity that is harder to handle by conventional computational tools and calls for more elaborate algorithms and the possible utilization of sophisticated devices.
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Notes
- 1.
If \(m<n_u\), then multiple solutions exist, so \(\mathbf {u}\) should be selected by means of an optimization problem. Equation (14.1b) implies the possible existence of uncontrollable flows \(\mathbf {d}\) at the junction nodes. Therefore, a subset of the control inputs will be restricted by the domain of some flow demands.
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Grosso, J.M., Ocampo-Martínez, C., Puig, V. (2017). Stochastic Model Predictive Control for Water Transport Networks with Demand Forecast Uncertainty. In: Puig, V., Ocampo-Martínez, C., Pérez, R., Cembrano, G., Quevedo, J., Escobet, T. (eds) Real-time Monitoring and Operational Control of Drinking-Water Systems. Advances in Industrial Control. Springer, Cham. https://doi.org/10.1007/978-3-319-50751-4_14
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