Region-free Explicit Model-Predictive Control for Linear Systems on Hilbert Spaces

In this article, we extend discrete-time explicit model-predictive control (MPC) rigorously to linear distributed parameter systems. After formulating an MPC framework and giving a relevant Karush-Kuhn-Tucker 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 partial differential equation with constraints, using a discrete-time explicit MPC controller.