Boundary Control of Shallow Water Waves

Efficient water management strategies protect our planet from potential climate catastrophes. To avert potential climate disasters, preserve the vital relationships between water, food, energy, and population growth, and maintain a delicate balance of living ecosystems, we must promote and implement efficient water management strategies at local, national, and global levels. Often, water is extracted for various purposes, whether through gate or dam manipulation, which can significantly impact the stability and health of ecosystems in the surrounding environment. The alteration of the flow regimes affects not only the natural flow in rivers but can cause substantial losses of natural habitats, and degrade water quality and temperature while inducing severe disruptions in diverse ecological processes that sustain biodiversity.

The primary focus of this talk is to address the challenges associated with managing water resources in human-engineered watercourses. First, I will discuss the design of observer-based boundary control strategies (including event-based boundary control), that guarantee exponential stability or exponential convergence for a class of coupled hyperbolic partial differential equations (PDEs) encompassing the well-known Saint-Venant equations. The second part of the talk addresses the stabilization of spatiotemporal dynamics of water and sediment layers in rivers under actuation. I will present results on the exponential stabilization of the sediment transport process with a continuous-time boundary control law.