  This paper proposes a method to compute finite abstractions that can be used
for synthesizing robust hybrid control strategies for nonlinear systems. Most
existing methods for computing finite abstractions utilize some global,
analytical function to provide bounds on the reachable sets of nonlinear
systems, which can be conservative and lead to spurious transitions in the
abstract systems. This problem is even more pronounced in the presence of
imperfect measurements and modelling uncertainties, where control synthesis can
easily become infeasible due to added spurious transitions. To mitigate this
problem, we propose to compute finite abstractions with robustness margins by
over-approximating the local reachable sets of nonlinear systems. We do so by
linearizing the nonlinear dynamics into linear affine systems and keeping track
of the linearization error. It is shown that this approach provides tighter
approximations and several numerical examples are used to illustrate of
effectiveness of the proposed methods.
