We present a connection between the viability kernel and maximal reachable sets. Current numerical schemes that compute the viability kernel suffer from a complexity that is exponential in the dimension of the state space. In contrast, extremely efficient and scalable techniques are available that compute maximal reachable sets. We show that under certain conditions these techniques can be used to conservatively approximate the viability kernel for possibly high-dimensional systems. We demonstrate the results on two practical examples, one of which is a seven-dimensional problem of safety in anesthesia.
In REF the authors made a relation between VK and maximal reachable sets, and used the already exiting Lagrangian techniques for computing the reachable sets to under-approximate the VK.
Computing the viability kernel using maximal reachable sets
HSCC '12
Mathematics Computer Science