Linear-Quadratic Optimal Control for Boundary Controlled Networks of Waves

Linear-quadratic (LQ) 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 paper 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.