@article{1140,
  keywords = {Resilient consensus, Computational geometry, Centerpoint, Fault tolerant networks},
  author = {Waseem Abbas and Mudassir Shabbir and Jiani Li and Xenofon Koutsoukos},
  title = {Resilient distributed vector consensus using centerpoint},
  abstract = {In this paper, we study the resilient vector consensus problem in networks with adversarial agents and improve resilience guarantees of existing algorithms. A common approach to achieving resilient vector consensus is that every non-adversarial (or normal) agent in the network updates its state by moving towards a point in the convex hull of its normal neighbors’ states. Since an agent cannot distinguish between its normal and adversarial neighbors, computing such a point, often called safe point, is a challenging task. To compute a safe point, we propose to use the notion of centerpoint, which is an extension of the median in higher dimensions, instead of the Tverberg partition of points, which is often used for this purpose. We discuss that the notion of centerpoint provides a complete characterization of safe points in Rd. In particular, we show that a safe point is essentially an interior centerpoint if the number of adversaries in the neighborhood of a normal agent i is less than Nid+1, where d is the dimension of the state vector and Ni is the total number of agents in the neighborhood of i. Consequently, we obtain necessary and sufficient conditions on the number of adversarial agents to guarantee resilient vector consensus. Further, by considering the complexity of computing centerpoints, we discuss improvements in the resilience guarantees of vector consensus algorithms and compare with the other existing approaches. Finally, we numerically evaluate our approach.},
  year = {2022},
  journal = {Automatica},
  volume = {136},
  pages = {110046},
  issn = {0005-1098},
  url = {https://www.sciencedirect.com/science/article/pii/S0005109821005744},
  doi = {https://doi.org/10.1016/j.automatica.2021.110046},
}