This paper addresses a robust periodic economic model predictive control (EMPC) based on interval arithmetic with unknown-but-bounded additive disturbances for the management of water distribution networks (WDNs). The system constraints in presence of system disturbances are tightened along the prediction horizon by means of the proposed interval arithmetic and considering that system variables in the WDN model are also subject to some algebraic equations. These algebraic equations should be satisfied when the disturbances have effects on those system variables. The EMPC controller is designed with adding the terminal state constraint. The periodically optimal steady states are obtained by employing a periodic EMPC planner with the nominal model. This periodic steady states are subsequently used to be terminal states. The on-line robust constraint satisfactions are implemented into the robust periodic EMPC controller. Finally, the proposed control strategy is verified using a case study.
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