The P-difference between two sets $\mathcal{A}$ and $\mathcal{B}$ is the set of all points, $\mathcal{C}$, such that the sum 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 set-theoretic control. In this paper, we show that an inner approximation of the P-difference between two sets described by collections of polynomial inequalities can be computed using Sums of Squares Programming. The effectiveness of the procedure is shown with some computational examples.

中文翻译：

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近似基本半代数集的庞特里亚金差分的基于平方和的过程

两组之间的 P 差 $\mathcal{一种}$ 和 $\mathcal{乙}$ 是所有点的集合， $\mathcal{C}$，使得总和 $\mathcal{乙}$ 到任何一点 $\mathcal{C}$ 包含在 $\mathcal{一种}$. 这种集差在鲁棒模型预测控制和集合论控制中起着重要作用。在本文中，我们表明可以使用平方和规划来计算由多项式不等式集合描述的两组之间 P 差的内近似。通过一些计算示例显示了该过程的有效性。