  Monitoring of hybrid systems attracts both scientific and practical
attention. However, monitoring algorithms suffer from the methodological
difficulty of only observing sampled discrete-time signals, while real
behaviors are continuous-time signals. To mitigate this problem of sampling
uncertainties, we introduce a model-bounded monitoring scheme, where we use
prior knowledge about the target system to prune interpolation candidates.
Technically, we express such prior knowledge by linear hybrid automata (LHAs) -
the LHAs are called bounding models. We introduce a novel notion of monitored
language of LHAs, and we reduce the monitoring problem to the membership
problem of the monitored language. We present two partial algorithms - one is
via reduction to reachability in LHAs and the other is a direct one using
polyhedra - and show that these methods, and thus the proposed model-bounded
monitoring scheme, are efficient and practically relevant.
