Robust Safety-Critical Control of Networked SIR Dynamics

Abstract

We present a robust safety-critical control framework tailored for networked susceptible-infected-recovered (SIR) epidemic dynamics, leveraging control barrier functions (CBFs) and robust control barrier functions to address the challenges of epidemic spread and mitigation. In our networked SIR model, each node must keep its infection level below a critical threshold, despite dynamic interactions with neighboring nodes and inherent uncertainties in the epidemic parameters and measurement errors, to ensure public health safety. We first derive a CBF-based controller that guarantees infection thresholds are not exceeded in the nominal case. We enhance the framework to handle realistic epidemic scenarios under uncertainties by incorporating compensation terms that reinforce safety against uncertainties: an independent method with constant bounds for uniform uncertainty, and a novel approach that scales with the state to capture increased relative noise in early or suppressed outbreak stages. Simulation results on a networked SIR system illustrate that the nominal CBF controller maintains safety under low uncertainty, while the robust approaches provide formal safety guarantees under higher uncertainties; in particular, the novel method employs more conservative control efforts to provide larger safety margins, whereas the independent approach optimizes resource allocation by allowing infection levels to approach the boundaries in steady epidemic regimes.