Data-Driven Permissible Safe Control with Barrier Certificates

TL;DR

This paper presents a data-driven approach to identify safe control strategies for stochastic systems with unknown dynamics, using Gaussian process learning and barrier certificates to ensure probabilistic safety.

Contribution

It introduces a novel algorithm that constructs stochastic barrier functions from data to find maximal safe control sets, enhancing safety in learning-enabled systems.

Findings

Increasing data size enlarges the safe strategy set.

Method guarantees probabilistic safety for the true system.

Applicable to both linear and nonlinear systems.

Abstract

This paper introduces a method of identifying a maximal set of safe strategies from data for stochastic systems with unknown dynamics using barrier certificates. The first step is learning the dynamics of the system via Gaussian process (GP) regression and obtaining probabilistic errors for this estimate. Then, we develop an algorithm for constructing piecewise stochastic barrier functions to find a maximal permissible strategy set using the learned GP model, which is based on sequentially pruning the worst controls until a maximal set is identified. The permissible strategies are guaranteed to maintain probabilistic safety for the true system. This is especially important for learning-enabled systems, because a rich strategy space enables additional data collection and complex behaviors while remaining safe. Case studies on linear and nonlinear systems demonstrate that increasing the size of the dataset for learning the system grows the permissible strategy set.