The P-difference between two sets $\mathcal{ A}$ and $\mathcal{ B}$ is the set of all points, $\mathcal{ C}$, such that the addition of $\mathcal{ B}$ to any of the points in $\mathcal{ C}$ is contained in $\mathcal{ A}$. Such a set difference plays an important role in robust model predictive control and in set-theoretic control. In the paper we demonstrate that an inner approximation of the P-difference between two semialgebraic sets can be computed using the Sums of Squares Programming, and we illustrate the procedure using several computational examples.
Categories: eess.SY cs.SY