1. What are the contributions mentioned in the paper "Computing the viability kernel using maximal reachable sets" ?
The authors present a connection between the viability kernel and maximal reachable sets.. The authors show that under certain conditions these techniques can be used to conservatively approximate the viability kernel for possibly high-dimensional systems.. The authors demonstrate the results on two practical examples, one of which is a seven-dimensional problem of safety in anesthesia.
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.](/figures/figure-1-iteratively-constructing-an-under-approximation-of-2lj8ou64.webp)
 (outlined in thick black lines via [30]) using Algorithm 1 under the double integrator dynamics. A finer time interval partition results in better approximation.](/figures/figure-2-for-the-set-k-red-k0-p-green-underapproximates-v-2lbw31sx.webp)
 for Example 5.2 for the first six states when z7 equals the setpoint value. The constraint set K (blue) and a piecewise ellipsoidal under-approximation of the provably safe regions (green) are shown.](/figures/figure-6-2d-projections-of-the-under-approximation-of-v-iab-3v4ttrti.webp)
 for Example 5.1. The flight envelope K is the red transparent region. The green piecewise ellipsoidal sets underapproximate the viability kernel.](/figures/figure-4-3d-projections-of-the-under-approximation-of-v-iab-1gz1urft.webp)
 for Example 5.1. The constraint set K (red) and a piecewise ellipsoidal under-approximation of the viability kernel (green) are shown. The level-set approximation of the viability kernel, computed via [30], is outlined in thick black lines.](/figures/figure-5-2d-projections-of-the-under-approximation-of-v-iab-25nrdqj4.webp)