Boundary Control of Quasi-Linear Hyperbolic Initial Boundary-Value Problem

The thesis presents different control design approaches for stabilizing
networks of quasi-linear hyperbolic partial differential equations. These
equations are usually conservative, which gives them interesting properties to
design stabilizing control laws.

Two main design approaches are developed: a methodology based on entropies and
Lyapunov functions and a methodology based on the Riemann invariants. The
stability theorems are illustrated using numerical simulations. Two practical
applications of these methodologies are presented. Network of navigation
channels are modelled using the Saint-Venant equation (also known as the
Shallow Water Equations). The stabilization problem of such system has an
industrial importance in order to satisfy the navigation constraints and to
optimize the production of electricity in hydroelectric plants, usually
located at each hydraulic gate. A second application deals with the regulation
of water waves in moving tanks. This problem is also modelled by a modified
version of the shallow water equations and appears in a number industrial
fields which deal with liquid moving parts.