Resilient Constrained Consensus over Complete Graphs via Feasibility Redundancy

Abstract: This paper considers a resilient high-dimensional constrained consensus problem and studies a resilient distributed algorithm for complete graphs. For convex constrained sets with a singleton intersection, a sufficient condition on feasibility redundancy and set regularity for reaching a desired consensus exponentially fast in the presence of Byzantine agents is derived, which can be directly applied to polyhedral sets. A necessary condition on feasibility redundancy for the resilient constrained consensus problem to be solvable is also provided.