  The reduction of constraints to obtain minimal representations of sets is a
very common problem in many engineering applications. While well-established
methodologies exist for the case of linear constraints, the problem of how to
detect redundant non-linear constraints is an open problem. In this paper we
present a novel methodology based on Sum of Squares for the elimination of
redundant polynomial constraints. The paper also presents some relevant
applications of the presented method to constrained control problems. In
particular, we show how the proposed method can be used in the Model Predictive
Control and in the Reference Governor frameworks to reduce the computational
burden of the online algorithms. Furthermore, this method can also be used to
eliminate the terminal constraints in MPC in a simple way that is independent
from the cost function.
