Abstract
We consider a sloped canal with friction that is governed by the Saint-Venant system with source term. We show that starting sufficiently close to a stationary constant subcritical initial state, we can control the system in finite time to a state in a C1 neighbourhood of any other stationary constant subcritical state by boundary control at the ends of the canal in such a way that during the process the system state remains continuously differentiable.Moreover, we show that if the derivative of the initial state is sufficiently small, it can be steered to every stationary constant subcritical state in finite time.
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