Global analytical model predictive control with input constraints

We derive a closed-form global analytical solution for model predictive control (MPC) of linear, discrete-time systems, subject to a quadratic performance index and hard magnitude constraints at the system input. The solution is shown to be a partition of the state space in regions for which an analytic expression is given for the corresponding control law. Both the regions and the control law are characterised in terms of the parameters of the open-loop optimal control problem that underlies MPC. The result exploits the geometric properties of quadratic programming