Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Safety-Critical Control of Networked SIR Dynamics

Saba Samadi, Brooks A. Butler, Philip E. Paré

TL;DR

This work addresses ensuring infection levels $x_i$ at each network node remain below thresholds $\bar{x}_i$ in a coupled SIR setting with uncertainty. It develops a node-level control barrier function (NCBF) controller for nominal safety and extends to robust CBFs (RCBFs) with compensation terms to handle disturbances, including a novel low-prevalence amplified uncertainty model. Theoretical guarantees via forward invariance are provided, along with two uncertainty schemes (independent and low-prevalence amplified) and proofs of robustness. Simulations on a 3-node network show nominal CBF safety under low noise and formal safety under higher uncertainty, with trade-offs between conservatism and resource use depending on the compensation strategy. The approach yields an explainable, safety-guaranteed framework for epidemic mitigation in networked populations, adaptable to varying uncertainty regimes and policy constraints.

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.

Robust Safety-Critical Control of Networked SIR Dynamics

TL;DR

This work addresses ensuring infection levels at each network node remain below thresholds in a coupled SIR setting with uncertainty. It develops a node-level control barrier function (NCBF) controller for nominal safety and extends to robust CBFs (RCBFs) with compensation terms to handle disturbances, including a novel low-prevalence amplified uncertainty model. Theoretical guarantees via forward invariance are provided, along with two uncertainty schemes (independent and low-prevalence amplified) and proofs of robustness. Simulations on a 3-node network show nominal CBF safety under low noise and formal safety under higher uncertainty, with trade-offs between conservatism and resource use depending on the compensation strategy. The approach yields an explainable, safety-guaranteed framework for epidemic mitigation in networked populations, adaptable to varying uncertainty regimes and policy constraints.

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.
Paper Structure (14 sections, 47 equations, 2 figures, 2 tables)

This paper contains 14 sections, 47 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Networked SIR Model Dynamics
  3. Problem Statement
  4. Nominal Safety‑Critical Control
  5. CBF Derivation
  6. Node Vulnerability Analysis
  7. Robust CBFs for the Networked SIR Model
  8. Uncertainty Bounded Independently of Control Input
  9. Low-Prevalence--Amplified Uncertainty
  10. Robust Safety Synthesis and Theoretical Guarantees
  11. Experiments and Results
  12. CBF under Nominal Conditions
  13. RCBF under Uncertainties
  14. Conclusion and Future Work

Figures (2)

  • Figure 1: Time evolution of the infected and recovered states in the networked SIR model under nominal conditions and with noise, along with the corresponding control inputs.
  • Figure 2: Time evolution of the infected and recovered states and control inputs in the noisy networked SIR model under independent and low-prevalence--amplified uncertainty.

Theorems & Definitions (3)

  • proof
  • proof
  • proof