A Smooth Robustness Measure of Signal Temporal Logic for Symbolic Control

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 natural language. Furthermore, STL specifications can be encoded cost functions using STL's robust semantics, transforming the synthesis problem into optimization problem. Unfortunately, these are non-smooth non-convex, exact solutions mixed-integer programming do not scale well. work has focused on smooth approximations robustness, which enable faster gradient-based methods find local maxima, at expense soundness and/or completeness. We propose novel robustness approximation that is everywhere, sound, asymptotically complete. Our approach combines benefits existing approximations, while enabling explicit tradeoff between conservativeness