Adversarial Robustness for Matrix Control Barrier Functions in Sampled-Data Systems

TL;DR

This paper develops theoretical guarantees for multi-agent safety using matrix control barrier functions in sampled-data systems, including adversarial scenarios and high relative degree extensions.

Contribution

It introduces new conditions for set invariance in sampled-data multi-agent systems with adversarial agents and extends results to high relative degree systems.

Findings

Conditions for safe set invariance with heterogeneous agents

Methods to ensure safety despite adversarial agents

Extensions to systems with high relative degree

Abstract

This paper presents novel theoretical results to guarantee multi-agent set invariance using Matrix Control Barrier Functions in sampled-data systems. More specifically, the paper presents conditions under which heterogeneous control-affine agents applying zero-order-hold control inputs can compute control inputs to render safe sets defined by matrix inequalities forward invariant. It then introduces methods to guarantee set invariance while accounting for the presence of adversarial agents seeking to drive the system state to unsafe sets. Finally, the paper presents theoretical extensions of these set invariance results to systems having high relative degree with respect to the matrix-valued safe set function.