Flatness-based trajectory planning for the shallow water equations

A flatness-based feed-forward control design approach for an open channel flow modelled by the shallow water equations is discussed. The control input consists of the adjustable height of opening of a delimiting sluice gate. In order to compute the trajectory of the control input, the physical boundaries containing the control input are neglected and the problem is reduced to an initial value problem w.r.t. the spatial coordinate. The solution to this problem can be obtained with the method of characteristics.