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In this paper, we present a mechanism for building hybrid system observers todifferentiate between specific positions of the hybrid system. The mechanism isdesigned through inferring metric temporal logic (MTL) formulae from simulatedtrajectories from the hybrid system. We first approximate the system behaviorby simulating finitely many trajectories with timerobust tube segments aroundthem. These time-robust tube segments account for both spatial and temporaluncertainties that exist in the hybrid system with initial state variations.The inferred MTL formulae classify different time-robust tube segments and thuscan be used for classifying the hybrid system behaviors in a provably correctfashion. We implement our approach on a model of a smart building testbed todistinguish two cases of room occupancy.

Temporal Logic Inference for Hybrid System Observation with Spatial and Temporal Uncertainties