Learning Robust Safety Controllers for Uncertain Input-Affine Polynomial Systems

TL;DR

This paper introduces a data-driven method to learn robust safety controllers for uncertain polynomial systems, enabling safety guarantees without explicit system modeling by utilizing observed data and SOS optimization.

Contribution

It presents a novel approach to synthesize robust control barrier certificates and safety controllers directly from data for unknown systems with disturbances.

Findings

Successfully guarantees safety in case studies

Operates without explicit system models

Effective under bounded disturbances

Abstract

This paper offers a direct data-driven approach for learning robust control barrier certificates (R-CBCs) and robust safety controllers (R-SCs) for discrete-time input-affine polynomial systems with unknown dynamics under unknown-but-bounded disturbances. The proposed method relies on data from input-state observations collected over a finite-time horizon while satisfying a specific rank condition to ensure the system is persistently excited. Our data-driven scheme enables the synthesis of R-CBCs and R-SCs directly from observed data, bypassing the need for explicit modeling of the system's dynamics and thus ensuring robust system safety against disturbances within an infinite time horizon. Our proposed approach is formulated as a sum-of-squares (SOS) optimization problem, providing a structured design framework. Two case studies showcase our method's capability to provide robust safety guarantees for unknown input-affine polynomial systems under bounded disturbances, demonstrating its practical effectiveness.