Boundary control of quasi-linear hyperbolic initial boundary-value problems

This 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. Netword of navigation channels are modelled using Saint-Venant equations (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 gates. 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 of industrial fields which deal with liquid moving parts.

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