Robust optimal control of one-reach open-channels

This paper is concerned with the regulation problem of open-channel hydraulic systems. More precisely the water flow and level within the reach are controlled trough the opening rates of two gates localized at each side of the reach. The hydrodynamics of such a system is governed by the non linear Saint-Venant partial differential equations. In the first part of the paper a reduction method which leads to a linear finite dimensional approximation model is shown to be convenient for control purposes. Then an original solution is proposed for the optimal regulation problem. This solution is designed to be robust to the approximation error. Finally, the existence of two very different time-scales in the problem is used to decouple the regulation of the reach and the regulations of the gates. The method is applied to a full non linear partial differential equations model.