  Recent years have seen an increasing use of Signal Temporal Logic (STL) as a
formal specification language for symbolic control, due to its expressiveness
and closeness to natural language. Furthermore, STL specifications can be
encoded as cost functions using STL's robust semantics, transforming the
synthesis problem into an optimization problem. Unfortunately, these cost
functions are non-smooth and non-convex, and exact solutions using
mixed-integer programming do not scale well. Recent work has focused on using
smooth approximations of robustness, which enable faster gradient-based methods
to find local maxima, at the expense of soundness and/or completeness. We
propose a novel robustness approximation that is smooth everywhere, sound, and
asymptotically complete. Our approach combines the benefits of existing
approximations, while enabling an explicit tradeoff between conservativeness
and completeness.
