Resilient Control of Dynamic Flow Networks Subject to Stochastic Cyber-Physical Disruptions

TL;DR

This paper develops resilient control strategies for dynamic flow networks affected by stochastic cyber-physical disruptions, enhancing throughput and network resiliency through novel Lyapunov functions and mode-dependent controls.

Contribution

It introduces new control methods for network resiliency under disruptions, including open-loop, mode-dependent, and closed-loop controls with throughput guarantees.

Findings

Existence of open-loop control achieving min-expected-cut capacity.

Mode-dependent control attains expected-min-cut capacity under observable disruptions.

Closed-loop control provides throughput guarantees for general networks.

Abstract

Modern network systems, such as transportation and communication systems, are prone to cyber-physical disruptions and thus suffer efficiency loss. This paper studies network resiliency, in terms of throughput, and develops resilient control to improve throughput. We consider single-commodity networks that admit congestion propagation. We also apply a Markov process to model disruption switches. For throughput analysis, we first use insights into congestion spillback to propose novel Lyapunov functions and then exploit monotone network dynamics to reduce computational costs of verifying stability conditions. For control design, we show that (i) for a network with infinite link storage space, there exists an open-loop control that attains the min-expected-cut capacity; (ii) for a network with observable disruptions that restrict maximum sending and/or receiving flows, there exists a mode-dependent control that attains the expected-min-cut capacity; (iii) for general networks, there exists a closed-loop control with throughput guarantees. We also derive lower bounds of resiliency scores for a set of numerical examples and verify resiliency improvement with our method.