Infinite-dimensional Receding Horizon Optimal Control for an Open-channel System

The paper deals with the receding horizon optimal control problem for an open hydraulic channel described by nonlinear partial differential equations (Saint-venant equations). The proposed development is based on an infinite dimensional linearized model of the system. From it, an appropriate Lyapunov function can be obtained (as in Coron et al. [2007]), which can be combined with the classical receding horizon approach for finite dimensional systems (see e.g. Findeisen and Allgower [2002] or Chen and Allgower [1998]), to end up with a value function which is indeed shown to decrease along the closed loop trajectories. The variational calculus is used to obtain the adjoint state, and the recently proposed Lattice Boltzmann method (see Zhou [2004], Chopard et al. [2009]) is used to solve both direct and adjoint partial differential equations. Finally, a simulation is carried out to validate the control.