Vertex based calculation of explicit MPC laws

We explore a new approach to calculating explicit solutions of linear-quadratic MPC problems with strictly convex cost. The central idea is to calculate the vertices of the state space polytopes, and to construct the pieces of the piecewise affine control law from only the vertices. We show that information calculated at the vertex suffices to infer the control laws that surround a given vertex. Consequently, it is not necessary to computationally construct and evaluate points in the interior of the polytopes. The approach only involves simple linear algebra such as rank testing and solving linear systems of equations. No assumptions are necessary regarding the facet-to-facet property. The approach has successfully been applied to a number of standard explicit MPC examples.