  We extend discrete-time explicit model predictive control (MPC) rigorously to
linear distributed parameter systems. After formulating an MPC framework and
giving a relevant KKT theorem, we realize fast regionless explicit MPC by using
the dual active set method QPKWIK. A Timoshenko beam with input and state
constraints is used to demonstrate the efficacy of the design at controlling a
continuous-time hyperbolic PDE with constraints, using a discrete-time explicit
MPC controller.
