The predictive control or Receding Horizon Optimal Control (RHOC) is becoming increasingly popular in many practical applications due to its significant advantages such as the stabilization and constraints handling. It has been well studied for finite dimensional systems even in the nonlinear case. However, its extension to infinite dimensional systems has not received much attention from researchers. This thesis proposes contributions on the application of this approach to systems of conservation laws. We present a complete proof of stability of RHOC for some classes of infinite dimensional systems. This result is then used for 2x2 hyperbolic systems with boundary control, and applied to an irrigation canal. We also propose the extension of this strategy to networks of cascaded 2x2 hyperbolic systems with an application to a set of connected irrigation canals. Furthermore, we study the benefits of RHOC in the context of nonlinear and semi-linear systems in particular with respect to the problem of shocks. All theoretical analyzes are validated by simulation in order to illustrate the effectiveness of the proposed approach.
