# Control from Signal Temporal Logic Specifications with Smooth Cumulative Quantitative Semantics

## TL;DR

This paper introduces a new smooth quantitative semantics for Signal Temporal Logic, enabling efficient control policy synthesis for nonlinear systems through gradient-based optimization and model predictive control, demonstrated in case studies.

## Contribution

It proposes a novel smooth and differentiable STL quantitative semantics called cumulative robustness, facilitating control synthesis via gradient ascent and model predictive control.

## Key findings

- Effective control policy synthesis for nonlinear systems using smooth STL semantics.
- Demonstrated advantages in long-horizon control through case studies.
- Integration of cumulative robustness with gradient-based optimization methods.

## Abstract

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 and differentiable 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 in order to synthesize control policies over long time horizons. The advantages of combining the cumulative robustness function with smooth optimization methods as well as model predictive control are illustrated in case studies.