A parameterized polyhedra approach for explicit constrained predictive control

The elaboration of an explicit description for the constrained model based predictive control laws is a useful alternative to the usually time-consuming on-line optimization methods. The paper presents a geometrical approach in this direction based on parameterized polyhedra. Subdomains in the parameters space and the correspondent linear affine laws are defined based on the parameterized vertices and their validity domains. The theoretical insight for the overall control law is brought through a double description (constraints-generators) of the feasible domain. The gain in computational effort is due to a hierarchic organization of the piecewise affine controllers.