  Linear-Quadratic optimal controls are computed for a class of boundary
controlled, boundary observed hyperbolic infinite-dimensional systems, which
may be viewed as networks of waves. The main results of this manuscript consist
in converting the infinite-dimensional continuous-time systems into
infinite-dimensional discrete-time systems for which the operators dynamics are
matrices, in solving the LQ-optimal control problem in discrete-time and then
in interpreting the solution in the continuous-time variables, giving rise to
the optimal boundary control input. The results are applied to two examples, a
small network of three vibrating strings and a co-current heat-exchanger, for
which boundary sensors and actuators are considered.
