Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics

We present a framework to synthesize control policies for nonlinear dynamical systems from complex temporal constraints specified in a rich temporal logic called Signal Temporal Logic (STL). We propose a novel smooth STL quantitative semantics called cumulative robustness, and efficiently compute control policies through a series of smooth optimization problems that are solved using gradient ascent algorithms. Furthermore, we demonstrate how these techniques can be incorporated in a model predictive control framework. The advantages of combining the cumulative robustness function with smooth optimization methods as well as model predictive control are illustrated in case studies.