  In this paper, we propose an approach for synthesizing provable reach-avoid
controllers, which drive a deterministic system operating in an unknown
environment to safely reach a desired target set. The approach falls within the
reachability analysis framework and is based on the computation of
inner-approximations of controlled reach-avoid sets(CRSs). Given a target set
and a safe set, the controlled reach-avoid set is the set of states such that
starting from each of them, there exists at least one controller to ensure that
the system can enter the target set while staying inside the safe set before
the target hitting time. Therefore, the boundary of the controlled reach-avoid
set acts as a barrier, which separating states capable of achieving the
reach-avoid objective from those that are not, and thus the computed
inner-approximation provides a viable space for the system to achieve the
reach-avoid objective. Our approach for synthesizing reach-avoid controllers
mainly consists of three steps. We first learn a safe set of states in the
unknown environment from sensor measurements based on a support vector machine
approach. Then, based on the learned safe set and target set, we compute an
inner-approximation of the CRS. Finally, we synthesize controllers online to
ensure that the system will reach the target set by evolving inside the
computed inner-approximation. The proposed method is demonstrated on a Dubin's
car system.
