Resilient Constrained Consensus over Complete Graphs via Feasibility Redundancy

TL;DR

This paper introduces a resilient distributed algorithm for high-dimensional constrained consensus over complete graphs, establishing conditions for exponential convergence despite Byzantine agents, and highlighting the importance of feasibility redundancy.

Contribution

It provides new sufficient and necessary conditions on feasibility redundancy for resilient consensus in high-dimensional constrained settings.

Findings

Exponential convergence under certain redundancy conditions

Applicable to convex and polyhedral constraint sets

Necessary and sufficient conditions for resilience established

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.