Risk-Awareness in Learning Neural Controllers for Temporal Logic Objectives

TL;DR

This paper presents a method for synthesizing neural network controllers that satisfy safety constraints expressed in Signal Temporal Logic while optimizing performance, using control barrier functions and risk measures to balance safety and efficiency.

Contribution

It introduces a novel approach to incorporate STL-based safety constraints into neural controller training using control barrier functions and risk-aware optimization.

Findings

Successfully applied to quad-rotor and unicycle examples.

Achieved safety and performance trade-offs with formal guarantees.

Demonstrated effectiveness on nonlinear control tasks.

Abstract

In this paper, we consider the problem of synthesizing a controller in the presence of uncertainty such that the resulting closed-loop system satisfies certain hard constraints while optimizing certain (soft) performance objectives. We assume that the hard constraints encoding safety or mission-critical task objectives are expressed using Signal Temporal Logic (STL), while performance is quantified using standard cost functions on system trajectories. In order to prioritize the satisfaction of the hard STL constraints, we utilize the framework of control barrier functions (CBFs) and algorithmically obtain CBFs for STL objectives. We assume that the controllers are modeled using neural networks (NNs) and provide an optimization algorithm to learn the optimal parameters for the NN controller that optimize the performance at a user-specified robustness margin for the safety specifications. We use the formalism of risk measures to evaluate the risk incurred by the trade-off between robustness margin of the system and its performance. We demonstrate the efficacy of our approach on well-known difficult examples for nonlinear control such as a quad-rotor and a unicycle, where the mission objectives for each system include hard timing constraints and safety objectives.