salle A. Turing CE4
1 June 2012 - 14h00
Scalable approximation of the viability kernel and safe control synthesis for LTI systems using maximal reachability
by Ian Mitchell from VERIMAG
Abstract: 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 three implementations using different set representations, and several examples. One of these set representations can be used to generate a nondeterministic hybrid control automaton which synthesizes a permissive but safe feedback control signal.