Control of hybrid automata with hidden modes: Translation to a perfect state information problem

In this paper, we consider the safety control problem for hybrid systems with hidden modes. In particular, we propose an approach to translate the control problem with imperfect mode information into an equivalent problem with perfect mode information. This approach is based on the notion of non-deterministic discrete information state as employed in the literature of games of imperfect information. We show that the safety control problems with imperfect information and perfect information are equivalent to each other under suitable detectability assumptions.