Resilient Distributed Vector Consensus Under Dynamic State Imprecision

In this paper, we study the resilient distributed vector consensus problem in networks where agents have imprecise knowledge of their neighbors’ states and operate in the presence of adversarial agents. Unlike existing methods that assume exact state observations, we consider a more realistic scenario where each normal agent’s knowledge of its neighbors’ states is restricted to a bounded region in R^d, referred to as the imprecision region. The size of this region reflects the degree of uncertainty and dynamically shrinks as agents update their states and approach consensus. We analyze the required decrease in the imprecision region at each iteration to ensure consensus, even in the presence of adversarial agents and state imprecision. By leveraging novel geometric insights, we present a method to ensure that each normal agent can consistently find a point within the convex hull of its normal neighbors’ true states, despite not knowing these states exactly. We also provide numerical evaluations to demonstrate the practical effectiveness of our approach in distributed optimization contexts.