Local Safety Filters for Networked Systems via Two-Time-Scale Design

TL;DR

This paper introduces a two-time-scale approach for implementing local safety filters in networked systems using Control Barrier Functions, enabling decentralized safety guarantees without subsystem coordination.

Contribution

It develops a novel local approximation method for networked CBF safety filters based on singular perturbation theory and derivative estimation, avoiding global communication.

Findings

Explicit bounds on safety mismatch are derived.

Trade-offs between safety, estimation errors, and activation time are characterized.

The approach enables decentralized safety guarantees in networked systems.

Abstract

Safety filters based on Control Barrier Functions (CBFs) provide formal guarantees of forward invariance, but are often difficult to implement in networked dynamical systems. This is due to global coupling and communication requirements. This paper develops locally implementable approximations of networked CBF safety filters that require no coordination across subsystems. The proposed approach is based on a two-time-scale dynamic implementation inspired by singular perturbation theory, where a small parameter $\epsilon$ separates fast filter dynamics from the plant dynamics; then, a local implementation is enabled via derivative estimation. Explicit bounds are derived to quantify the mismatch between trajectories of the systems with dynamic filter and with the ideal centralized safety filter. These results characterize how safety degradation depends on the time-scale parameter $\epsilon$, estimation errors, and filter activation time, thereby quantifying trade-offs between safety guarantees and local implementability.