  Symbolic models or abstractions are known to be powerful tools for the
control design of cyber-physical systems (CPSs) with logic specifications. In
this paper, we investigate a novel learning-based approach to the construction
of symbolic models for nonlinear control systems. In particular, the symbolic
model is constructed based on learning the un-modeled part of the dynamics from
training data based on state-space exploration, and the concept of an
alternating simulation relation that represents behavioral relationships with
respect to the original control system. Moreover, we aim at achieving safe
exploration, meaning that the trajectory of the system is guaranteed to be in a
safe region for all times while collecting the training data. In addition, we
provide some techniques to reduce the computational load, in terms of memory
and computation time, of constructing the symbolic models and the safety
controller synthesis, so as to make our approach practical. Finally, a
numerical simulation illustrates the effectiveness of the proposed approach.
