On the continuity and complexity of control laws based on multiparametric linear programs

The present paper proposes a geometrical approach for the multiparametric linear programs (mp-LP). The interest for this topic is motivated by the need for explicit formulations in the constrained predictive control (with non-quadratic cost indexes). It is shown how the double description of the feasible domains can offer access to the entire family of optimal mappings from the parameters space to the arguments space. Further the explicit solutions with guarantee of continuity and optimality are studied