Observations on the complexity of the explicit MPC

This paper analyzes the structure of the constrained optimization problem induced by a typical Model Predictive Control (MPC) problem. The main idea is to exploit the particularities of the feasible domain (namely, that input/state/output constraints describe in fact zonotopic sets) to: i) efficiently describe the solution as a piecewise affine function with polyhedral support; ii) exploit the combinatorial properties of zonotopes to reduce the number of candidate active sets. The results are tested over a numerical example.