Robust boundary control of systems of conservation laws: theoretical study with numerical and experimental validations

The stability problem of a system of conservation laws perturbed by non-homogeneous terms is investigated. These non-homogeneous terms are assumed to have a small C1-norm. By a Riemann coordinates approach a sufficient stability criterion is established in terms of the boundary conditions. This criterion can be interpreted as a robust stability condition to design a boundary control for Systems of conservation laws subject to external disturbances. This stability result is then applied to the problem of the regulation of the water level and the flow rate in an open channel. The flow in the channel is described by the shallow water equations perturbed by small non-homogeneous terms due to the effects of the bottom slope, the slope's friction and also of the lateral supply. The Boundary actions are defined as the position of both spillways located at the extremities of the reach. It is assumed that only the height of the flow is measured at both extremities. The stability result is validated both by simulating on a real river data and by experimenting on a micro-channel setup.