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arXiv · 2008.06126

A Sum-of-Squares-Based Procedure to Approximate the Pontryagin Difference of Semialgebraic Sets

Andres Cotorruelo·Ilya Kolmanovsky·Emanuele Garone
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Abstract

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.

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Andres Cotorruelo, Ilya Kolmanovsky, Emanuele Garone. 2020-08-13. A Sum-of-Squares-Based Procedure to Approximate the Pontryagin Difference of Semialgebraic Sets. https://arxiv.org/abs/2008.06126

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