This article presents the design of a control strategy for the Calais canal, a navigation canal located in a lowland area in northern France that is affected by tides. Moreover, the available actuators are discrete-valued and the hierarchy of operational objectives is time-varying. All these circumstances render water level regulation of the Calais canal a challenging problem. In view of this situation, the design of the overall control architecture is divided into a sequence of structured tasks, which are distributed among layers. The upper layer determines the current operating mode based on the analysis of several environmental and operational aspects. Information regarding the current mode is taken into account at the intermediate layer to select the appropriate optimization-based control problem, which is solved using lexicographic minimization. The optimal control setpoints are determined and sent to the lower layer, where scheduling problems are solved to select low-level control actions from a finite set to minimize the mismatch with respect to the optimal setpoints. Different realistic simulation scenarios are tested to demonstrate the effectiveness of the proposed approach.

This paper presents the design of a model predictive control (MPC) for the Calais canal, located in the north of France for satisfactory management of the system. To estimate the unknown inputs/outputs arising from the uncontrolled pumps, a digital twin (DT) in the framework of a Matlab-SIC2 is used to reproduce the dynamics of the canal, and the real database corresponding to a period of three days is employed to evaluate the control strategy. The canal is characterized by two operating modes due to high and low tides. As a consequence of this, time-varying constraints on the use of gates must be considered, which leads to the design of two multiobjective control problems, one for the high tide and another for the low tide. Furthermore, a moving horizon estimation (MHE) strategy is used to provide the MPC with unmeasured states. The simulation results show that the different objectives are met satisfactorily.

This paper presents the design of a model predictive scheduling strategy to address the inland waterborne transport (IWT) problem considering bridges that must open to enable vessel passage. The main contribution is the formulation of a control-oriented model of the problem, including propositional logic expressions that characterize system behavior and their conversion into (in)equality constraints. The resulting model is embedded into a predictive scheduling approach to determine bridge opening timetables and vessel passage times in a coordinated manner. The effectiveness of the strategy is demonstrated on a realistic case study based on the Rhine-Alpine corridor.

Model Predictive Control (MPC) has recently gained increasing interest in the adaptive management of water resources systems due to its capability of incorporating disturbance forecasts into real-time optimal control problems. Yet, related literature is scattered with heterogeneous applications, case-specific problem settings, and results that are hardly generalized and transferable across systems. Here, we systematically review 149 peer-reviewed journal articles published over the last 25 years on MPC applied to water reservoirs, open channels, and urban water networks to identify common trends and open challenges in research and practice. The three water systems we consider are inter-connected, multi-purpose and multi-scale dynamical systems affected by multiple hydro-climatic uncertainties and evolving socioeconomic factors. Our review first identifies four main challenges currently limiting most MPC applications in the water domain: (i) lack of systematic benchmarking of MPC with respect to other control methods; (ii) lack of assessment of the impact of uncertainties on the model-based control; (iii) limited analysis of the impact of diverse forecast types, resolutions, and prediction horizons; (iv) under-consideration of the multi-objective nature of most water resources systems. We then argue that future MPC applications in water resources systems should focus on addressing these four challenges as key priorities for future developments.

This paper presents a switched linear system representation of water canal dynamics to incorporate different operating modes, which arise due to the occurrence of extreme weather phenomena such as flooding and drought episodes. To guarantee the stability during mode switching, a proper analysis on permanence regions-given by a collection of equilibrium states-for the switched linear system is presented. The permanence region is computed within a compact set, which depends on an adequate level region for the canals. A suitable algorithm is used to formulate an asymptotic stable Model Predictive Control (MPC) that steers and maintains the states of the system inside the target region indefinitely in a feasible manner. This strategy is successfully tested in a simulation using a realistic model of a canal.

Model predictive control (MPC) has been widely employed to control a large variety of water systems, such as dams, irrigation canals, inland waterways, drinking water networks and wastewater treatment plants. Its predictive capabilities and the possibility to incorporate constraints make MPC well suited to address several, and sometimes opposite, management objectives linked to water systems. The design of MPC for water systems is usually performed via dedicated software (e.g., Matlab) and tested in simulation using dedicated hydraulic software. However, the implementation of MPC strategies in real systems requires additional development to allow for its embedding within the information systems that are used by system managers. A possible solution is to create a tool based on Python that can be easily integrated with the information systems of managers, and within which existing Matlab solutions can be incorporated. In this paper, the development a ready-to-use Python tool using a hierarchical MPC approach designed for the management of the Calais Canal is presented.

This work is concerned with the design of a two-step distributed state estimation scheme for large-scale systems in the presence of unknown-but-bounded disturbances and noise. The set-membership approach is employed to construct a compact set containing the states consistent with system measurements and bounded noise and disturbances. The tightened feasible region is then provided to a moving horizon estimator that determines the optimal state estimates. Partitioning of the overall problem and coordination of the resulting subproblems are achieved using decomposition of the optimality conditions and community detection. The proposed strategy is tested on a case study based on a reactor–separator system widely used in the literature. Its performance is compared to those of centralized and distributed (without set-membership) implementations, allowing to highlight its effectiveness.

This work presents the design of a combined control and state estimation approach to simultaneously maintain optimal water levels and maximize hydroelectricity generation in inland waterways using gates and ON/OFF pumps. The latter objective can be achieved by installing turbines within canal locks, which harness the energy generated during lock filling and draining operations. Hence, the two objectives are antagonistic in nature, as energy generation maximization results from optimizing the number of lock operations, which in turn causes unbalanced upstream and downstream water levels. To overcome this problem, a two-layer control architecture is proposed. The upper layer receives external information regarding the current tidal period, and determines control actions that maintain optimal navigation conditions and maximize energy production using model predictive control (MPC) and moving horizon estimation (MHE). This information is provided to the lower layer, in which a scheduling problem is solved to determine the activation instants of the pumps that minimize the error with respect to the optimal pumping references. The strategy is applied to a realistic case study, using a section of the inland waterways in northern France, which allows to showcase its efficacy.

This paper proposes a combined control and state estimation strategy for inland waterways, aiming at simultaneously attaining the optimal water level management and maximizing hydroelectricity generation. The latter can be realized by turbines installed in canal locks that harness the energy generated during lock filling and draining operations. These two objectives are of opposed nature, as maximization of energy generation can be achieved by maximizing the number of lock operations, which in turn leads to unbalanced water levels upstream and downstream of the lock. To address this issue, the multi-objective optimization problem is formulated. Then, model predictive control (MPC) and moving horizon estimation (MHE) are designed to maintain navigation conditions in the canals while maximizing energy production. Finally, the proposed strategy is applied to a realistic case study based on part of the inland waterways in the north of France.

This paper considers the inland waterborne transport (IWT) problem, and presents a scheduling approach for inland vessels and locks to generate optimal vessel and lock timetables. The scheduling strategy is designed in the switching max-plus-linear (SMPL) systems framework, as these are characterized by a number of features that make them well suited to represent the IWT problem. In particular, the resulting model is linear in the max-plus algebra, and SMPL systems can switch between modes, an interesting feature due to the presence of vessel routing and ordering constraints in the model. Moreover, SMPL systems can be transformed into mixed-integer linear programming (MILP) problems, for which efficient solvers are available. Finally, a realistic case study is used to test the approach and assess its effectiveness.

This paper presents an adaptive approximation-based scheme for learning a partially known ship power propulsion plant under various environmental conditions. Considering the effect of water depth on the engine power, a dynamic model is defined comprised of the engine dynamics and the 1-DoF ship manoeuvring dynamics. The modelling challenge is the determination of ship resistance. To meet this challenge analytical modelling of ship resistance is combined with an error-filtering online learning (EFOL) scheme for computing an approximation of the unmodeled part of ship resistance related to wind and air. After simulations under multiple weather conditions, the trained model was demonstrated to efficiently estimate the unmodelled part of the ship resistance for an inland vessel.

This paper addresses the problem of guaranteeing efficient inland waterway transport in the presence of sequential movable bridges, which must be operated to grant vessel passage. The main contribution is the formulation of the vessel passage scheduling problem as a mixedinteger programming problem. The scheduling algorithm receives vessel widths and voyage plans, and determines feasible vessel passage through bridges that best matches vessel plans. Process optimization is carried out using a rolling horizon implementation to keep the problem computationally tractable in real-time applications. Finally, a realistic case study based on the Rhine-Alpine corridor is used to test the approach and demonstrate its effectiveness.