Control Barrier Functions for Unknown Nonlinear Systems using Gaussian Processes

TL;DR

This paper presents a method combining Gaussian processes and control barrier functions to safely control unknown nonlinear systems, providing probabilistic safety guarantees and demonstrating effectiveness on a jet engine example.

Contribution

The paper introduces a systematic approach to synthesize safety controllers for unknown nonlinear systems using Gaussian process learning and control barrier functions with probabilistic safety guarantees.

Findings

Successfully synthesized a safety controller for a jet engine example.

Provided a probabilistic lower bound on safety satisfaction.

Demonstrated the effectiveness of the approach in a practical scenario.

Abstract

This paper focuses on the controller synthesis for unknown, nonlinear systems while ensuring safety constraints. Our approach consists of two steps, a learning step that uses Gaussian processes and a controller synthesis step that is based on control barrier functions. In the learning step, we use a data-driven approach utilizing Gaussian processes to learn the unknown control affine nonlinear dynamics together with a statistical bound on the accuracy of the learned model. In the second controller synthesis steps, we develop a systematic approach to compute control barrier functions that explicitly take into consideration the uncertainty of the learned model. The control barrier function not only results in a safe controller by construction but also provides a rigorous lower bound on the probability of satisfaction of the safety specification. Finally, we illustrate the effectiveness of the proposed results by synthesizing a safety controller for a jet engine example.