Infinite-dimensional nonlinear predictive control design for open-channel hydraulic systems
Résumé
A nonlinear predictive control design based on Saint Venant equations is presented in this paper in order to regulate both water depth and water flow rate in a single pool of an open-channel hydraulic system. Thanks to variational calculus, some necessary optimality conditions are given. The adjoint partial differential equations of Saint Venant partial differential equations are also derived. The resulting two-point boundary value problem is solved numerically by using both time and space discretization and operator approximations based on nonlinear time-implicit finite differences. The practical effectiveness of the control design is demonstrated by a simulation example. A extension of the predictive control scheme to a multi-pool system is proposed by using a decomposition-coordination approach based on two-level algorithm and the use of an augmented Lagrangian, which can take advantage of communication networks used for distributed control. This approach may be easily applied to other problems governed by hyperbolic PDEs, such as road traffic systems.