  This paper introduces a sampling-based strategy synthesis algorithm for
nondeterministic hybrid systems with complex continuous dynamics under temporal
and reachability constraints. We model the evolution of the hybrid system as a
two-player game, where the nondeterminism is an adversarial player whose
objective is to prevent achieving temporal and reachability goals. The aim is
to synthesize a winning strategy -- a reactive (robust) strategy that
guarantees the satisfaction of the goals under all possible moves of the
adversarial player. Our proposed approach involves growing a (search) game-tree
in the hybrid space by combining sampling-based motion planning with a novel
bandit-based technique to select and improve on partial strategies. We show
that the algorithm is probabilistically complete, i.e., the algorithm will
asymptotically almost surely find a winning strategy, if one exists. The case
studies and benchmark results show that our algorithm is general and effective,
and consistently outperforms state of the art algorithms.
