题目：PDE Backstepping Control of Shallow Water Waves: Application to a River Sedimentation Problem
报告人：Mamadou Diagne assistant professor （Rensselaer Polytechnic Institute）
摘要：Global warming is drastically altering rainfall patterns, increasing the risk of expensive floods and water scarcity.These contingencies are further accentuated by the rapid conversion of natural landscapes to urbanized areas that are continuallygrowing in population. Sustainable management strategies are becoming critical to ensure the optimum use of an essential but limited water resource on the planet. Often, river infrastructures such as dams, gates and reservoirs are built to satisfy human societies’ water and energy demand. However, the maintenance of costly engineered rivers’ infrastructures is still posing crucial problems related to reservoirs sedimentation and ecosystems preservation. Using backstepping design,exponential stabilization of the linearized Saint-Venant-Exner (SVE) model of water dynamics in a sediment-filled canal with arbitrary values of canal bottom slope, friction, porosity, and water-sediment interaction, is achieved. The linearized SVE model consists of two rightward convecting transport Partial Differential Equations (PDEs) and one leftward convecting transport PDE.A single boundary input control strategy with actuation located only at the downstream gate is employed. A full state feedback controller is designed which guarantees exponential stability of the desired setpoint of the resulting closed-loop system. Using the reconstruction of the distributed state through a backstepping observer, an output feedback controller is established, resulting in the exponential stability of the closed-loop system at the desired setpoint. The proposed state and output feedback controllers can deal with both subcritical and supercritical flow regimes without any restrictive conditions.
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