We propose an approach to compute inner and outer-approximations of the sets of values satisfying constraints expressed as arbitrarily quantified formulas. Such formulas arise for instance when specifying important problems in control such as robustness, motion planning or controllers comparison. We propose an interval-based method which allows for tractable but tight approximations. We demonstrate its applicability through a series of examples and benchmarks using a prototype implementation.

翻译：我们提出了一种方法，用于计算满足任意量化公式约束的值集的内外近似。这类公式出现在控制领域中的关键问题中，例如鲁棒性、运动规划或控制器比较等。我们提出了一种基于区间的方法，能够实现易于处理且紧致的近似。通过原型实现的系列示例和基准测试，我们展示了该方法的适用性。