  We present a predictive feedback control method for a class of quasilinear
hyperbolic systems with one boundary control input. Assuming exact model
knowledge, convergence to the origin, or tracking at the uncontrolled boundary,
are achieved in finite time. A robustness certificate is provided, showing that
at least under more restrictive assumptions on the system coefficients, the
control method has inherent robustness properties with respect to small errors
in the model, measurements and control input. Rigorous, although conservative
conditions on the time derivative of the initial condition and on the design
parameter controlling the convergence speed are given to ensure global
existence of the solution for initial conditions with arbitrary infinity-norm.
