  Formal design of embedded and cyber-physical systems relies on mathematical
modeling. In this paper, we consider the model class of hybrid automata whose
dynamics are defined by affine differential equations. Given a set of
time-series data, we present an algorithmic approach to synthesize a hybrid
automaton exhibiting behavior that is close to the data, up to a specified
precision, and changes in synchrony with the data. A fundamental problem in our
synthesis algorithm is to check membership of a time series in a hybrid
automaton. Our solution integrates reachability and optimization techniques for
affine dynamical systems to obtain both a sufficient and a necessary condition
for membership, combined in a refinement framework. The algorithm processes one
time series at a time and hence can be interrupted, provide an intermediate
result, and be resumed. We report experimental results demonstrating the
applicability of our synthesis approach.
