Neural Control Barrier Functions for Signal Temporal Logic Specifications with Input Constraints

TL;DR

This paper introduces a neural network-based framework for synthesizing time-varying control barrier functions to ensure complex STL-specified tasks are safely achieved by dynamical systems under input constraints.

Contribution

It proposes a novel neural control barrier function approach that incorporates STL specifications and input constraints, with formal safety guarantees.

Findings

Successfully synthesizes controllers for STL tasks in simulations.

Ensures safety and task fulfillment under input constraints.

Demonstrates effectiveness on various dynamical systems.

Abstract

Signal Temporal Logic (STL) provides a powerful framework to describe complex tasks involving temporal and logical behavior in dynamical systems. This work addresses controller synthesis for continuous-time systems subject to STL specifications and input constraints. We propose a neural network-based framework for synthesizing time-varying control barrier functions (TVCBF) and their corresponding controllers for systems to fulfill a fragment of STL specifications while respecting input constraints. We formulate barrier conditions incorporating the spatial and temporal logic of the given STL specification. We also incorporate a method to refine the time-varying set that satisfies the STL specification for the given input constraints. Additionally, we introduce a validity condition to provide formal safety guarantees across the entire state space. Finally, we demonstrate the effectiveness of the proposed approach through several simulation studies considering different STL tasks for various dynamical systems (including affine and non-affine systems).