Geometric Methods for Resilient Aggregation and Safe Point Computation in Adversarial Multiagent Networks With Imprecise Data

This paper studies resilient data aggregation in multiagent networks subject to both adversarial agents and imprecise state observations. We show that existing algorithms, which assume exact state information, fail under such dual uncertainty. To address this, we propose a geometric approach that models each agent's state as an imprecision region (in <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbb {R}^{d}$</tex-math></inline-formula>) containing the true state. We present the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Centerpoint of Imprecision Hulls (CPIH)</i> algorithm, which takes these regions-some corresponding to adversarial agents-as inputs and computes a point guaranteed to lie within the convex hull of the normal agents' true states, despite unknown adversary identities and true state locations. We thoroughly analyze the algorithm's theoretical guarantees and apply it to the resilient distributed vector consensus problem. Furthermore, we extend the framework to dynamic settings where these regions shrink as agents move closer together, deriving sufficient conditions for exact consensus in a multiagent network despite access to only imprecise states and adversarial presence. Numerical evaluations validate the method's effectiveness.