Guaranteed approximations of arbitrarily quantified reachability problems

TL;DR

This paper introduces an interval-based method to compute tight inner and outer approximations of value sets satisfying arbitrarily quantified formulas, applicable to control problems like robustness and motion planning.

Contribution

It presents a novel approach for approximating complex quantified constraints in control problems, enabling tractable analysis with tight bounds.

Findings

Effective in computing tight approximations

Applicable to control problems like robustness and motion planning

Demonstrated through examples and benchmarks

Abstract

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.