Optimal Control for Networks with Unobservable MaliciousNodes

Abstract Classic network optimization theory focuses on network models with stochastic dynamics and all nodes being observable and controllable. However, modern network systems often offer limited access and suffer from adversarial attacks. In this paper, we focus on networks with unobservable malicious nodes, where the network dynamics, such as external arrivals and control actions of malicious nodes can be adversarial. We first extend the existing adversarial network models by introducing a new maliciousness metric that constrains the dynamics of the adversary, and characterize the stability region of a network under adversarial dynamics. We then propose an algorithm that only operates on the accessible nodes and does not require direct observations of the malicious nodes, and show that our algorithm is stabilizing as long as the network dynamics are within the stability region. Finally, we show that our algorithm stabilizes the network even if the estimates of the network state are erroneous, and characterize the necessary and sufficient conditions for networks with unobservable malicious nodes to be stabilizable when subjected to estimation errors.