Local Safety Filters for Networked Systems via Two-Time-Scale Design
For networked control systems, this work provides a practical method to achieve safety guarantees with reduced communication, though the guarantees are approximate and degrade with local approximations.
The paper develops locally implementable safety filters for networked systems using a two-time-scale design, enabling each subsystem to enforce safety without coordination. It derives explicit bounds on safety degradation as a function of the time-scale parameter and estimation errors.
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 $ε$ 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 $ε$, estimation errors, and filter activation time, thereby quantifying trade-offs between safety guarantees and local implementability.