Optimal control of complex irrigation systems via decomposition-coordination and the use of augmented Lagrangian

In this paper, we consider the optimal control problem for complex irrigation systems, using a receding horizon. The idea of decomposition is introduced for the goal of both reducing the computational complexity, to comply with the system topology and the monitoring architecture. A decomposition-coordination algorithm based on the use of both an augmented Lagrangian and the duplication of variables is developed which is suitable for the optimal control of complex irrigation systems, composed of water retention systems, water supply/distribution systems using canals and pipe networks. In some conventional decomposition-coordination approaches, such as the price decomposition-coordination algorithm, the coupling constraints between subsystems or the associated Lagrange multipliers are used as coordination variables. In our case, some physical variables, such as water flow rates, are duplicated in each subsystem, where they appear. Some compatibility constraints are then introduced and their associated Lagrange multipliers are used as coordination variables. In this paper, we present the application of this approach to to the Canal de la Bourne irrigation network, which irrigates the agricultural plain of Valence (south-east of France).